SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Mechanics, EXT2 M1 SM-Bank 5

A student throws a ball for his dog to retrieve. The position vector of the ball, relative to an origin at ground level seconds after release, is given by  . Displacement components are measured in metres, where is a unit vector to the east, is a unit vector to the north and is a unit vector vertically up.

Calculate the total vertical distance, in metres, travelled by the ball before it hits the ground. Give your answer correct to one decimal place.   (3 marks)

Show Answers Only

Show Worked Solution


  

Mechanics, EXT2 M1 2023 HSC 12c

An object with mass kilograms slides down a smooth inclined plane with velocity , where is the time in seconds after the object started sliding down the plane. The inclined plane makes an angle with the horizontal, as shown in the diagram. The normal reaction force is . The acceleration due to gravity is and has magnitude . No other forces act on the object.

The vectors and are unit vectors parallel and perpendicular, respectively, to the plane, as shown in the diagram.
 

  1. Show that the resultant force on the object is  .  (2 marks)

  2. Given that the object is initially at rest, find its velocity in terms of , and .  (2 marks)

Show Answers Only

i.   

ii.   

Show Worked Solution

i.       
         


 

♦ Mean mark (i) 50%.

ii.   

 
 
 
   

 

Mechanics, EXT2* M1 2007 HSC 2d

A skydiver jumps from a hot air balloon which is 2000 metres above the ground. The velocity, metres per second, at which she is falling    seconds after jumping is given by  .

  1. Find her acceleration ten seconds after she jumps. Give your answer correct to one decimal place.  (2 marks)

  2. Find the distance that she has fallen in the first ten seconds. Give your answer correct to the nearest metre.  (2 marks)

Show Answers Only
Show Worked Solution
i.     
   
 
   
   

 

 
 
 

 

ii.