Calculating Time to Hit the Ground for a Movie Stunt Car

How long does it take for the full-size remote-controlled car to hit the ground below?

Given data: height of the cliff = 9.81 m, initial velocity of the car = 18.34 m/s

Answer:

The time it takes for the car to hit the ground below is 1.414 seconds.

When solving for the time it takes for the car to hit the ground below, we can use the following kinematic equation:

y_f = y_i + v_it + 0.5at²

where:

y_f = final height

y_i = initial height

v_i = initial velocity

t = time taken

a = acceleration due to gravity (approx. 9.81 m/s²)

Plugging in the values from the data:

9.81 = 0 + 18.34*t + 0.5*9.81*t²

Simplifying the equation, we get:

4.905t² + 18.34t - 9.81 = 0

Using the quadratic formula to solve for t, we get:

t = (-18.34 ± √(18.34²-4*4.905*(-9.81)))/(2*4.905)

t = (-18.34 ± 22.68)/(9.81)

t ≈ 1.414 seconds

Therefore, it takes approximately 1.414 seconds for the full-size remote-controlled car to hit the ground below after being driven off the 9.81 m tall cliff at 18.34 m/s.