Question

C. How far horizontally from the cliff will the car land?

Answer 1

Given data

*The given mass of the car is m = 885 kg

*The given speed is u = 40 m/s

*The given acceleration of the car is a = 3 m/s^2

*The given distance is s = 200 m

*The height of the cliff is H = 120 m

(a)

The formula for the time taken by the car is given by the equation of motion as

`s=ut+(1)/(2)at^2`

Substitute the values in the above expression as

`\begin{gathered} 200=(40)t+(1)/(2)*3* t^2 \\ 200=40t+1.5t^2 \\ t=4.30\text{ s} \end{gathered}`

Hence, the time taken by the car is t = 4.30 s

(b)

The formula for the time taken by the car to land is given as

`T=\sqrt[]{(2H)/(g)}`

*Here g is the acceleration due to the gravity

Substitute the values in the above expression as

`\begin{gathered} T=\sqrt[]{(2*120)/(9.8)} \\ =4.94\text{ s} \end{gathered}`

Hence, the time taken by the car to land is T = 4.94 s

(c)

The formula for the horizontal distance from the cliff is given as

`R=u* T`

Substitute the values in the above expression as

`\begin{gathered} R=(40)(4.94) \\ =197.6\text{ m} \end{gathered}`

Hence, the horizontal distance from the cliff is R = 197.6 m