Answer:
104.6 m
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 [tex]v_x = 13 m/s[/tex], and this is constant during the entire motion, as there are no forces in the horizontal direction
[tex]d=60 m[/tex] is the horizontal distance travelled by the car
Therefore, we can find the total time of flight of the car:
[tex]t=\frac{d}{v_x}=\frac{60}{13}=4.62 s[/tex]
Now we analyze the vertical motion, which is a free fall motion, so we can use the suvat equation:
[tex]s=ut+\frac{1}{2}at^2[/tex]
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
[tex]a=g=9.8 m/s^2[/tex] is the acceleration of gravity
Solving for s, we find the height of the cliff:
[tex]s=0+\frac{1}{2}(9.8)(4.62)^2=104.6 m[/tex]
