Aussie Maths & Science Teachers: Save your time with SmarterEd
The brightness of a lamp \((L)\) is measured in lumens and varies directly with the square of the voltage \((V)\) applied, which is measured in volts.
When the lamp runs at 7 volts, it produces 735 lumens.
What voltage is required for the lamp to produce 1820 lumens? Give your answer correct to one decimal place. (3 marks)
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`11.2\ \text(volts)`
`L prop V^2\ \ => \ \ L=kV^2`
`text(Find)\ k\ \text{given}\ L = 735\ \text{when}\ V = 7:`
| `735` | `= k xx 7^2` |
| `:. k` | `= 735/49=15` |
`text(Find)\ V\ text(when)\ L = 1820:`
| `1820` | `= 15 xx V^2` |
| `V^2` | `= 1820/15=121.33…` |
| `V` | `= sqrt{121.33} = 11.2\ text(volts)\ \ text{(to 1 d.p.)}` |
Taylor discovers that for a Spotted stingray, its mass is directly proportional to the square of its wingspan.
One Spotted stingray has a wingspan of 60 cm and a mass of 5400 grams.
What is the expected wingspan of a Spotted stingray with a mass of 9.6 kg? (3 marks)
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`80.0\ text{cm}`
`text(Mass) prop text(wingspan)^2\ \ =>\ \ m = kw^2`
`text(Find)\ k:`
| `5400` | `= k xx 60^2` |
| `k` | `= 5400/60^2= 1.5` |
`text(Find)\ w\ text(when)\ \ m = 9600:`
| `9600` | `= 1.5 xx w^2` |
| `w^2` | `= 9600/1.5=6400` |
| `:. w` | `= 80\ text{cm}` |
The stopping distance of a motor bike, in metres, is directly proportional to the square of its speed in km/h, and can be represented by the equation
`text{stopping distance}\ = k xx text{(speed)}^2`
where `k` is the constant of variation.
The stopping distance for a motor bike travelling at 40 km/h is 16 m.
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a. `k=0.01`
b. `64.0\ text{m}`
a. `text{stopping distance}\ = k xx text{(speed)}^2`
| `16` | `=k xx 40^2` | |
| `k` | `=16/40^2=0.001` |
b. `text{Find stopping distance}\ (d)\ text{when speed = 80 km/h:}`
`d=0.01 xx 80^2=64.0\ text{m}`