# Physics Problem: Remote-Controlled Car Cliff Drop

## How long does it take the remote-controlled car to hit the ground below the cliff?

a) 0.589 s

b) 1.57 s

c) 1.836 s

d) 1.4185 s

e) None of these is correct.

## Final Answer:

In this physics problem, we can find the time it takes for the car to hit the ground by using a quadratic equation derived from the equations of motion. The answer is 2.1755 s.

To find how long it takes for the remote-controlled car to hit the ground below the cliff, we can use the equation of motion: \[ d = vit + \frac{1}{2}at^2 \] where: - \( d \) is the distance (10.05 m), - \( vi \) is the initial velocity (24.63 m/s), - \( a \) is the acceleration due to gravity (-9.8 m/s^2), and - \( t \) is the time we're trying to find.

Plugging in the values given in the data: \[ 10.05 = 24.63t - \frac{1}{2}(9.8)t^2 \] Rearranging the equation and solving for \( t \), we get a quadratic equation: \[ 4.9t^2 - 24.63t + 10.05 = 0 \]

Using the quadratic formula, we find two solutions for \( t \): 0.4185 s and 2.1755 s. Since we're looking for the time it takes for the car to hit the ground, we choose the longer solution, which is 2.1755 s.

Understanding and solving physics problems involving motion and equations are essential skills for students studying physics. By practicing more problems like this, you can deepen your understanding of the concepts and improve your problem-solving abilities.