Question

A+car+accidently+rolls+off+a+cliff.As+it+leaves+the+cliff+it+has+a+horizontal+velocity+of+13+m/s,it+hits+the+ground+60m+from+the+shoreline.+Calculate+the+height+of+the+cliff.

Answer 1

104.6 m

Step-by-step explanation:

The motion of the car is a projectile motion, consisting of:

- A horizontal motion at constant speed

- A vertical motion at constant acceleration (acceleration of gravity)

We know that:

The initial horizontal velocity of the car is
`v_x = 13 m/s`, and this is constant during the entire motion, as there are no forces in the horizontal direction

`d=60 m` is the horizontal distance travelled by the car

Therefore, we can find the total time of flight of the car:

`t=(d)/(v_x)=(60)/(13)=4.62 s`

Now we analyze the vertical motion, which is a free fall motion, so we can use the suvat equation:

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

where

s is the vertical displacement (= the height of the cliff)

u = 0 is the initial vertical velocity

t = 4.62 s is the time of flight

`a=g=9.8 m/s^2` is the acceleration of gravity

Solving for s, we find the height of the cliff:

`s=0+(1)/(2)(9.8)(4.62)^2=104.6 m`