GEOMETRY, FUR1-NHT 2019 VCAA 6 MC
A cake in the shape of three cylindrical sections is shown in the diagram below.
Each section of the cake has a height of 8 cm, as shown in the diagram.
The middle section of the cake, B, has twice the volume of the top section of the cake, A.
The bottom section of the cake, C, has twice the volume of the middle section of the cake, B.
The volume of the top section of the cake, A, is 900 cm3.
The diameter of the bottom section of the cake, C, in centimetres, is closest to
- 12
- 18
- 24
- 36
- 48
GEOMETRY, FUR1-NHT 2019 VCAA 5 MC
The cities of Lima and Washington, DC have the same longitude of 77° W.
The shortest great circle distance between Lima and Washington, DC is 5697 km.
Assume that the radius of Earth is 6400 km.
Lima has a latitude of 12° S and is located due south of Washington, DC.
What is the latitude of Washington, DC?
- 39° N
- 51° S
- 51° N
- 63° N
- 65° S
GEOMETRY, FUR1-NHT 2019 VCAA 4 MC
GEOMETRY, FUR1-NHT 2019 VCAA 3 MC
A waterfall in a national park is 4 km east of a camp site.
A lookout tower is 4 km south of the waterfall.
The bearing of the camp site from the lookout tower is
- 045°
- 090°
- 135°
- 300°
- 315°
GEOMETRY, FUR1-NHT 2019 VCAA 2 MC
Which one of the following locations is closest to the Greenwich meridian?
- 32° S, 40° E
- 32° S, 80° E
- 32° S, 60° W
- 32° S, 120° E
- 32° S, 160° W
GEOMETRY, FUR1-NHT 2019 VCAA 1 MC
GRAPHS, FUR1-NHT 2019 VCAA 8 MC
Jamie sold bottles of homemade lemonade to his neighbours on Saturday.
The revenue, in dollars, he made from selling `n` bottles of lemonade is given by
revenue = 3.5`n`
The cost, in dollars, of making `n` bottles of lemonade is given by
cost = 60 + `n`
The profit made by Jamie on Saturday could have been
- $162
- $165
- $168
- $173
- $177
GRAPHS, FUR1-NHT 2019 VCAA 7 MC
The shaded area in the graph below represents the feasible region for a linear programming problem.
The maximum value of the objective function `Z = -2x - 2y` occurs at
- point `C` only.
- any point along line segment `BC`.
- any point along line segment `AD`.
- any point along line segment `AB`.
- any point along line segment `DC`.
GRAPHS, FUR1-NHT 2019 VCAA 6 MC
In January 2018, an online shop had 260 customer accounts.
In June 2018, the shop had 500 customer accounts.
The graph below shows the number of customer accounts, `a`, with the online shop `n` months after January 2018, for a period of 10 months.
The growth in the number of customer accounts that this graph shows is expected to continue beyond these 10 months, following the same trend.
How many customer accounts can the online shop expect to have at the end of December 2019 `(n = 23)`?
- 1364
- 1376
- 1388
- 1400
- 1412
GRAPHS, FUR1-NHT 2019 VCAA 5 MC
The revenue, `R`, in dollars, that a company receives from selling `n` caps is given by the equation
`R = {(25n, qquad n <= 1000),(20n + c, qquad n> 1000):}`
The graph of this revenue equation consists of two straight lines that intersect at the point where `n = 1000`.
What is the value of `c` in this revenue equation?
- 0
- 1000
- 2000
- 4000
- 5000
GRAPHS, FUR1-NHT 2019 VCAA 4 MC
A farm has `x` cows and `y` sheep.
On this farm there are always at least twice as many sheep as cows.
The relationship between the number of cows and the number of sheep on this farm can be represented by the inequality
- `x <= y/2`
- `y <= x/2`
- `2x >= y`
- `2y >= x`
- `xy >= 2`
GRAPHS, FUR1-NHT 2019 VCAA 3 MC
GRAPHS, FUR1-NHT 2019 VCAA 2 MC
Two straight lines have the equations `3x - 2y = 3` and `-2x + 5y = 9`.
These lines have one point of intersection.
Another line that also passes through this point of intersection has the equation
- `y = -x`
- `y = x`
- `y = -2x`
- `y = 2x`
- `y = 3x`
GRAPHS, FUR1-NHT 2019 VCAA 1 MC
Mechanics, SPEC2-NHT 2019 VCAA 5
A pallet of bricks weighing 500 kg sits on a rough plane inclined at an angle of `α°` to the horizontal, where `tan(α°) = (7)/(24)`. The pallet is connected by a light inextensible cable that passes over a smooth pulley to a hanging container of mass `m` kilograms in which there is 10 L of water. The pallet of bricks is held in equilibrium by the tension `T` newtons in the cable and a frictional resistance force of 50 `g` newtons acting up and parallel to the plane. Take the weight force exerted by 1 L of water to be `g` newtons.
- Label all forces acting on both the pallet of bricks and the hanging container on the diagram above, when the pallet of bricks is in equilibrium as described. (1 mark)
- Show that the value of `m` is 80. (3 marks)
Suddenly the water is completely emptied from the container and the pallet of bricks begins to slide down the plane. The frictional resistance force of 50 `g` newtons acting up the plane continues to act on the pallet.
- Find the distance, in metres, travelled by the pallet after 10 seconds. (3 marks)
- When the pallet reaches a velocity of `3\ text(ms)^-1`, water is poured back into the container at a constant rate of 2 L per second, which in turn retards the motion of the pallet moving down the plane. Let `t` be the time, in seconds, after the container begins to fill.
- i. Write down, in terms of `t`, an expression for the total mass of the hanging container and the water it contains after `t` seconds. Give your answer in kilograms. (1 mark)
- ii. Show that the acceleration of the pallet down the plane is given by `(text(g)(5 - t))/(t + 290)\ text(ms)^-2` for `t ∈[0, 5)`. (2 marks)
- iii. Find the velocity of the pallet when `t = 4`. Give your answer in metres per second, correct to one decimal place. (2 marks)
Mechanics, SPEC2-NHT 2019 VCAA 15 MC
A lift accelerates from rest at a constant rate until it reaches a speed of 3 ms−1. It continues at this speed for 10 seconds and then decelerates at a constant rate before coming to rest. The total travel time for the lift is 30 seconds.
The total distance, in metres, travelled by the lift is
- 30
- 45
- 60
- 75
- 90
Mechanics, SPEC2-NHT 2019 VCAA 17 MC
A ball is thrown vertically upwards with an initial velocity of `7sqrt6` ms−1, and is subject to gravity and air resistance. The acceleration of the ball is given by `overset(¨)x = −(9.8 + 0.1v^2)`, where `v` ms−1 is its velocity when it is at a height of `x` metres above ground level.
The maximum height, in metres, reached by the ball is
- `5log_e(4)`
- `log_e(sqrt31)`
- `(5pisqrt2)/21`
- `5log_e(2)`
- `(7pisqrt2)/3`
Mechanics, SPEC2-NHT 2019 VCAA 16 MC
An object of mass 2 kg is travelling horizontally in a straight line at a constant velocity of magnitude 2 ms−1. The object is hit in such a way that it deflects 30° from its original path, continuing at the same speed in a straight line.
The magnitude, correct to two decimal places, of the change of momentum, in kg ms−1, of the object is
- 0.00
- 0.24
- 1.04
- 1.46
- 2.07
Mechanics, SPEC1-NHT 2019 VCAA 1
A 10 kg mass is placed on a rough plane that inclined at 30° to the horizontal, as shown in the diagram below. A force of 40 N is applied to the mass up the slope and parallel to the slope. There is also a frictional resistance force of magnitude `F` that opposes the motion of the mass.
- Find the magnitude of the frictional resistance force, in newtons, acting up the slope if the force is just sufficient to stop the mass from sliding down the slope. (2 marks)
- An additional force of magnitude `P` newtons is applied to the mass up the slope and parallel to the slope. The sum of the additional force and the frictional resistance force of magnitude `F` that now acts down the slope is such that it is just sufficient to stop the mass from sliding up the slope. (2 marks)
GRAPHS, FUR2 2019 VCAA 3
Members of the association will travel to a conference in cars and minibuses:
- Let `x` be the number of cars used for travel.
- Let `y` be the number of minibuses used for travel.
- A maximum of eight cars and minibuses in total can be used.
- At least three cars must be used.
- At least two minibuses must be used.
The constraints above can be represented by the following three inequalities.
`text(Inequality 1) qquad qquad x + y <= 8`
`text(Inequality 2) qquad qquad x >= 3`
`text(Inequality 3) qquad qquad y >= 2`
- Each car can carry a total of five people and each minibus can carry a total of 10 people.
A maximum of 60 people can attend the conference.
Use this information to write Inequality 4. (1 mark)
The graph below shows the four lines representing Inequalities 1 to 4.
Also shown on this graph are four of the integer points that satisfy Inequalities 1 to 4. Each of these integer points is marked with a cross (✖).
- On the graph above, mark clearly, with a circle (o), the remaining integer points that satisfy Inequalities 1 to 4. (1 mark)
Each car will cost $70 to hire and each minibus will cost $100 to hire.
- What is the cost for 60 members to travel to the conference? (1 mark)
- What is the minimum cost for 55 members to travel to the conference? (1 mark)
- Just before the cars were booked, the cost of hiring each car increased.
The cost of hiring each minibus remained $100.
All original constraints apply.
If the increase in the cost of hiring each car is more than `k` dollars, then the maximum cost of transporting members to this conference can only occur when using six cars and two minibuses.
Determine the value of `k`. (1 mark)
GRAPHS, FUR2 2019 VCAA 2
Each branch within the association pays an annual fee based on the number of members it has.
To encourage each branch to find new members, two new annual fee systems have been proposed.
Proposal 1 is shown in the graph below, where the proposed annual fee per member, in dollars, is displayed for branches with up to 25 members.
- What is the smallest number of members that a branch may have? (1 mark)
- The incomplete inequality below shows the number of members required for an annual fee per member of $10.
Complete the inequality by writing the appropriate symbol and number in the box provided. (1 mark)
3 ≤ number of members |
|
Proposal 2 is modelled by the following equation.
annual fee per member = – 0.25 × number of members + 12.25
- Sketch this equation on the graph for Proposal 1, shown below. (1 mark)
- Proposal 1 and Proposal 2 have the same annual fee per member for some values of the number of members.
Write down all values of the number of members for which this is the case. (1 mark)
GRAPHS, FUR2 2019 VCAA 1
The graph below shows the membership numbers of the Wombatong Rural Women’s Association each year for the years 2008–2018.
- How many members were there in 2009? (1 mark)
-
- Show that the average rate of change of membership numbers from 2013 to 2018 was − 6 members per year. (1 mark)
- If the change in membership numbers continues at this rate, how many members will there be in 2021? (1 mark)
GEOMETRY, FUR2 2019 VCAA 3
The following diagram shows a crane that is used to transfer shipping containers between the port and the cargo ship.
The length of the boom, `BC`, is 25 m. The length of the hoist, `AB`, is 15 m.
-
- Write a calculation to show that the distance `AC` is 20 m. (1 mark)
- Find the angle `ACB`.
Round your answer to the nearest degree. (1 mark)
- The diagram below shows a cargo ship next to a port. The base of a crane is shown at point `Q`.
The base of the crane (`Q`) is 20 m from a shipping container at point `R`. The shipping container will be moved to point `P`, 38 m from `Q`. The crane rotates 120° as it moves the shipping container anticlockwise from `R` to `P`.
What is the distance `RP`, in metres?
Round your answer to the nearest metre. (1 mark)
- A shipping container is a rectangular prism.
Four chains connect the shipping container to a hoist at point `M`, as shown in the diagram below.
The shipping container has a height of 2.6 m, a width of 2.4 m and a length of 6 m.
Each chain on the hoist is 4.4 m in length.
What is the vertical distance, in metres, between point `M` and the top of the shipping container?
Round your answer to the nearest metre. (2 marks)
GEOMETRY, FUR2 2019 VCAA 2
A cargo ship travels from Magadan (60° N, 151° E) to Sydney (34° S, 151° E).
- Explain, with reference to the information provided, how we know that Sydney is closer to the equator than Magadan. (1 mark)
- Assume that the radius of Earth is 6400 km.
Find the shortest great circle distance between Magadan and Sydney.
Round your answer to the nearest kilometre. (1 mark)
- The cargo ship left Sydney (34° S, 151° E) at 6 am on 1 June and arrived in Perth (32° S, 116° E) at 10 am on 11 June.
There is a two-hour time difference between Sydney and Perth at that time of year.
How many hours did it take the cargo ship to travel from Sydney to Perth? (1 mark)
GEOMETRY, FUR2 2019 VCAA 1
The following diagram shows a cargo ship viewed from above.
The shaded region illustrates the part of the deck on which shipping containers are stored.
- What is the area, in square metres, of the shaded region? (1 mark)
Each shipping container is in the shape of a rectangular prism.
Each shipping container has a height of 2.6 m, a width of 2.4 m and a length of 6 m, as shown in the diagram below.
- What is the volume, in cubic metres, of one shipping container? (1 mark)
- What is the total surface area, in square metres, of the outside of one shipping container? (1 mark)
- One shipping container is used to carry barrels. Each barrel is in the shape of a cylinder.
Each barrel is 1.25 m high and has a diameter of 0.73 m, as shown in the diagram below.
Each barrel must remain upright in the shipping container
`qquad qquad`
What is the maximum number of barrels that can fit in one shipping container? (1 mark)
GRAPHS, FUR1 2019 VCAA 8 MC
Jenny and Alan’s house is 900 m from a supermarket.
Jenny is at the house and Alan is at the supermarket.
At 12 noon Jenny leaves the house and walks towards the supermarket.
At the same time, Alan leaves the supermarket and walks towards the house.
Jenny’s planned walk is modelled by the equation
`j = {(qquad 120t, qquad qquad 0 < t <= 2), (100t + 40, qquad qquad 2 < t <= 6), (65t + 250, qquad qquad 6 < t <= 10):}`
where `j` is Jenny’s distance, in metres, from the house after `t` minutes.
Alan’s planned walk is modelled by the equation
`a= -80t + 900 qquad qquad t > 0`
where `a` is Alan’s distance, in metres, from the house after `t` minutes.
When they meet
- Jenny will have walked 359 m, to the nearest metre.
- Alan will have walked 360 m, to the nearest metre.
- Alan will have walked 382 m, to the nearest metre.
- Alan will have walked 518 m, to the nearest metre.
- Jenny will have walked 541 m, to the nearest metre.
GRAPHS, FUR1 2019 VCAA 7 MC
The feasible region for a linear programming problem is shaded in the diagram below.
The equation of the objective function for this problem is of the form
`P = mx + ny`, where `m > 0` and `n > 0`
The dotted line passing through the points `V` and `W` in the diagram has the same slope as the objective function for this problem.
The minimum value of the objective function can be determined by calculating its value at
- point `S` only.
- point `T` only.
- point `U` only.
- any point along the line segment `RU`.
- any point along the line segment `ST`.
GRAPHS, FUR1 2019 VCAA 6 MC
A recipe for a fruit drink lists both pineapple juice and mango juice.
Let `x` be the number of millilitres of pineapple juice required to make the fruit drink.
Let `y` be the number of millilitres of mango juice required to make the fruit drink.
For every 200 mL of mango juice that is used, at least 300 mL of pineapple juice must be used.
The inequality representing this situation is
- `x <= (2y)/3`
- `x <= (3y)/2`
- `y <= (2x)/3`
- `y <= (3x)/2`
- `y <= (2x)/5`
GRAPHS, FUR1 2019 VCAA 5 MC
Giovanni makes and sells toy train sets.
Each toy train set costs $40.00 to make and sells for $65.00
Giovanni also has a fixed cost for making a batch of toy train sets.
Last Sunday, Giovanni sold a batch of 35 toy train sets for a profit of $250.
Giovanni’s fixed cost for this batch of train sets is
- $250
- $625
- $875
- $1400
- $2275
GRAPHS, FUR1 2019 VCAA 4 MC
GRAPHS, FUR1 2019 VCAA 3 MC
A shop sells two types of discs: compact discs (CDs) and digital video discs (DVDs).
CDs are sold for $7.00 each and DVDs are sold for $13.00 each.
Bonnie bought a total of 16 discs for $178.00
How many DVDs did Bonnie buy?
- 3
- 5
- 7
- 9
- 11
GRAPHS, FUR1 2019 VCAA 2 MC
The cost, `$C`, of using `K` kilowatt hours of electricity can be calculated using the equation below.
`C = 52.00 + 0.15 xx K`
From this equation, it can be concluded that there is
- no fixed charge and the electricity used is charged at $0.15 per kilowatt hour.
- no fixed charge and the electricity used is charged at $52.00 per kilowatt hour.
- a fixed charge of $0.15 and the electricity used is charged at $52.00 per kilowatt hour.
- a fixed charge of $52.00 and the electricity used is charged at $0.15 per kilowatt hour.
- a fixed charge of $52.00 and the electricity used is charged at $15.00 per kilowatt hour.
GRAPHS, FUR1 2019 VCAA 1 MC
GEOMETRY, FUR1 2019 VCAA 8 MC
GEOMETRY, FUR1 2019 VCAA 7 MC
A can of dog food is in the shape of a cylinder. The can has a circumference of 18.85 cm and a volume of 311 cm³.
The height of the can, in centimetres, is closest to
- 2.8
- 3.0
- 6.0
- 11.0
- 16.5
GEOMETRY, FUR1 2019 VCAA 6 MC
All cities in China are in the same time zone.
Wuhan (31° N, 114° E) and Chengdu (31° N, 104° E) are both cities in China.
On one day in January, the sun set in Wuhan at 5.50 pm.
Assuming that 15° of longitude equates to a one-hour time difference, the time the sun set in Chengdu on the same day is
- 4.20 pm
- 5.10 pm
- 5.50 pm
- 6.30 pm
- 7.20 pm
GEOMETRY, FUR1 2019 VCAA 5 MC
In triangle `ABC`, the point `D` lies on the line `AC`, as shown in the diagram below.
The length of the line `BC` is equal to the length of the line `BD`.
Which one of the following statements is true?
- The angle `BAD` is equal to the angle `ADB`.
- The angle `ADB` is equal to the angle `BDC`.
- The sum of the angle `ACB` and the angle `ADB` is equal to 180°.
- The sum of the angle `ABD` and the angle `CBD` is equal to 180°.
- The sum of the angle `ABC` and the angle `ACB` is equal to the angle `ADB`.
GEOMETRY, FUR1 2019 VCAA 4 MC
Triangle `M`, shown below, has side lengths of 3 cm, 4 cm and 5 cm.
Four other triangles have the following side lengths:
-
- Triangle `N` has side lengths of 3 cm, 6 cm and 8 cm.
- Triangle `O` has side lengths of 4 cm, 8 cm and 12 cm.
- Triangle `P` has side lengths of 6 cm, 8 cm and 10 cm.
- Triangle `Q` has side lengths of 9 cm, 12 cm and 15 cm.
The triangles that are similar to triangle `M` are
- triangle `N` and triangle `O`.
- triangle `N`, triangle `O` and triangle `P`.
- triangle `O` and triangle `P`.
- triangle `O` and triangle `Q`.
- triangle `P` and triangle `Q`.
GEOMETRY, FUR1 2019 VCAA 3 MC
GEOMETRY, FUR1 2019 VCAA 2 MC
GEOMETRY, FUR1 2019 VCAA 1 MC
The four bases of a baseball field form four corners of a square of side length 27.43 m, as shown in the diagram below.
A player ran from home base to first base, then to second base, then to third base and finally back to home base.
The minimum distance, in metres, that the player ran is
- 27.43
- 54.86
- 82.29
- 109.72
- 164.58
Mechanics, SPEC2 2019 VCAA 5
A mass of `m_1` kilograms is initially held at rest near the bottom of a smooth plane inclined at `theta` degrees to the horizontal. It is connected to a mass of `m_2` kilograms by a light inextensible string parallel to the plane, which passes over a smooth pulley at the end of the plane. The mass `m_2` is 2 m above the horizontal floor.
The situation is shown in the diagram below.
- After the mass `m_1` is released, the following forces, measured in newtons, act on the system:
• weight forces `W_1` and `W_2`
• the normal reaction force `N`
• the tension in the string `T`
On the diagram above, show and clearly label the forces acting on each of the masses. (1 mark)
- If the system remains in equilibrium after the mass `m_1` is released, show that `sin(theta) = (m_2)/(m_1)`. (1 mark)
- After the mass `m_1` is released, the mass `m_2` falls to the floor.
- For what values of `theta` will this occur? Express your answer as an inequality in terms of `m_1` and `m_2`. (1 mark)
- Find the magnitude of acceleration, in ms−2, of the system after the mass `m_1` is released and before the mass `m_2` hits the floor. Express your answer in terms of `m_1, \ m_2` and `theta`. (2 marks)
- After the mass `m_1` is released, it moves up the plane.
Find the maximum distance, in metres, that the mass `m_1` will move up the plane if `m_1 = 2m_2` and `sin(theta) = 1/4`. (5 marks)
Mechanics, SPEC2 2019 VCAA 17 MC
A particle is held in equilibrium by three coplanar forces of magnitudes `F_1, F_2` and `F_3`.
The angles between these forces are `alpha, beta` and `gamma` as shown in the diagram below.
If `beta = 2alpha`, then `(F_1)/(F_2)` is equal to
- `1/2 sin(alpha)`
- `2sin(alpha)`
- `1/2text(cosec)(alpha)`
- `1/2cos(alpha)`
- `1/2sec(alpha)`
Mechanics, SPEC2 2019 VCAA 14 MC
A 4 kg mass is held at rest on a smooth surface. It is connected by a light inextensible string that passes over a smooth pulley to a 2 kg mass, which in turn is connected by the same type of string to a 1 kg mass. This is shown in the diagram below.
When the 4 kg mass is released, the tension in the string connecting the 1 kg and 2 kg masses is `T` newtons. The value of `T` is
- `(4g)/7`
- `(3g)/7`
- `g/7`
- `(6g)/7`
- `g`
Mechanics, SPEC1 2019 VCAA 9
- A light inextensible string is connected at each end to a horizontal ceiling. A mass of `m` kilograms hangs in equilibrium from a smooth ring on the string, as shown in the diagram below. The string makes an angle `alpha` with the ceiling.
`qquad qquad`
Express the tension, `T` newtons, in the string in terms of `m`, `g` and `alpha`. (1 mark) - A different light inextensible sting is connected at each end to a horizontal ceiling. A mass of `m` kilograms hangs from a smooth ring on the string. A horizontal force of `F` newtons is applied to the ring. The tension in the sting has a constant magnitude and the system is in equilibrium. At one end the string makes an angle `beta` with the ceiling and at the other end the string makes an angle `2beta` with the ceiling, as shown in the diagram below.
Show that `F = mg((1 - cos(beta))/(sin(beta)))`. (3 marks)
Mechanics, SPEC2 2012 VCAA 22 MC
Mechanics, SPEC2 2012 VCAA 21 MC
A particle of mass 3 kg is acted on by a variable force, so that its velocity `v` m/s when the particle is `x` m from the origin is given by `v = x^2`.
The force acting on the particle when `x = 2`, in newtons, is
A. 4
B. 12
C. 16
D. 36
E. 48
Mechanics, SPEC2 2012 VCAA 20 MC
Mechanics, SPEC2 2012 VCAA 14 MC
A particle is acted on by two forces, one of 6 newtons acting due south, the other of 4 newtons acting in the direction N60° W.
The magnitude of the resultant force, in newtons, acting on the particle is
- `10`
- `2sqrt7`
- `2sqrt19`
- `sqrt(52 - 24sqrt3)`
- `sqrt(52 + 24sqrt3)`
Mechanics, SPEC2 2011 VCAA 21 MC
A constant force of magnitude `F` newtons accelerates a particle of mass 2 kg in a straight line from rest to 12 ms`\ ^(−1)` over a distance of 16 m.
It follows that
- `F` = 4.5
- `F` = 9.0
- `F` = 12.0
- `F` = 18.0
- `F` = 19.6
Mechanics, SPEC1 2011 VCAA 7
A flowerpot of mass `m` kg is held in equilibrium by two light ropes, both of which are connected to a ceiling. The first rope makes an angle of 30° to the vertical and has tension `T_1` newtons. The second makes an angle of 60° to the vertical and has tension `T_2` newtons.
- Show that `T_2 = T_1/sqrt 3.` (1 mark)
- The first rope is strong, but the second rope will break if the tension in it exceeds 98 newtons.
Find the maximum value of `m` for which the flowerpot will remain in equilibrium. (3 marks)
Mechanics, SPEC2 2013 VCAA 21 MC
A particle of mass 2 kg moves in a straight line with an initial velocity of 20 m/s. A constant force opposing the direction of the motion acts on the particle so that after 4 seconds its velocity is 2 m/s.
The magnitude of the force, in newtons, is
A. 4.5
B. 6
C. 9
D. 18
E. 36
Mechanics, SPEC2 2013 VCAA 20 MC
A 5 kg parcel is on the floor of a lift that is accelerating downwards at 3 m/s².
The reaction, in newtons, of the floor of the lift on the parcel is
A. `−15 + 5g`
B. `15 + 5g`
C. `−15 + 3g`
D. `−15 − 5g`
E. `15 + 3g`
Mechanics, SPEC2 2013 VCAA 16 MC
Forces of magnitude 5 N, 7 N and `Q` N act on a particle that is in equilibrium, as shown in the diagram below.
The magnitude of `Q`, in newtons, can be found by evaluating
A. `sqrt(5^2 + 7^2 - 2 xx 5 xx 7 cos(70^@))`
B. `5^2 + 7^2 - 2 xx 5 xx 7 cos(110^@)`
C. `sqrt(5^2 + 7^2 - 2 xx 5 xx 7 cos(110^@))`
D. `5^2 + 7^2 - 2 xx 5 xx 7 cos(70^@)`
E. `sqrt(5^2 + 7^2 - 2 xx 5 xx 7 cos(20^@))`
Mechanics, SPEC1 2013 VCAA 1
Mechanics, SPEC2 2014 VCAA 20 MC
Particles of mass 3 kg and 5 kg are attached to the ends of a light inextensible string that passes over a fixed smooth pulley, as shown above. The system is released from rest.
Assuming the system remains connected, the speed of the 5 kg mass after two seconds is
A. 4.0 m/s
B. 4.9 m/s
C. 9.8 m/s
D. 10.0 m/s
E. 19.6 m/s
Mechanics, SPEC2 2014 VCAA 18 MC
A body on a horizontal smooth plane is acted upon by four forces, `underset ~F_1`, `underset ~F_2`, `underset ~F_3` and `underset ~F_4` as shown.
The force `underset ~F_1` acts in a northerly direction and the force `underset ~F_4` acts in a westerly direction.
Given that `|\ underset ~F_1\ | = 1`, `|\ underset ~F_2\ | = 2`, `|\ underset ~F_3\ | = 4` and `|\ underset ~F_4\ | = 5`, the motion of the body is such that it
A. is in equilibrium.
B. moves to the west.
C. moves to the north.
D. moves in the direction 30° south of west.
E. moves to the east.
Mechanics, SPEC2 2015 VCAA 19 MC
Mechanics, SPEC2 2015 VCAA 16 MC
The diagram above shows a mass suspended in equilibrium by two light strings that make angles of `60^@` and `30^@` with a ceiling. The tensions in the strings are `T_1` and `T_2`, and the weight force acting on the mass is `underset~W`. The correct statement relating the given forces is
A. `underset~T_1 + underset~T_2 + underset~W = underset~0`
B. `underset~T_1 + underset~T_2 - underset~W = underset~0`
C. `underset~T_1 xx 1/2 + underset~T_2 xx sqrt3/2 = underset~0`
D. `underset~T_1 xx sqrt3/2 + underset~T_2 xx 1/2 = underset~W`
E. `underset~T_1 xx 1/2 + underset~T_2 xx sqrt3/2 = underset~W`
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