Drive Off the Cliff: The Stunt Car Adventure

How far from the base of the cliff does the stunt car land?

A) 55.0 meters
B) 60.5 meters
C) 70.0 meters
D) 75.0 meters

Answer:

The stunt car lands approximately 75.0 meters from the base of the cliff, which corresponds to option D.

The problem is solved using the equations for vertical and horizontal projectile motions. The time for the car to hit the ground is first calculated using the vertical distance and gravity, which is then used with the car's horizontal velocity to find the horizontal distance from the cliff.

This problem is a horizontal projectile motion problem, a topic covered in Physics. For horizontal projectile motion, the horizontal component of distance is given by D = V * t, where V is velocity and t is time. However, to find time, you need to consider the vertical motion.

Here, a stunt car falls a vertical distance of 85.0 m. We can use the equation of motion h = 1/2 * g * t^2, where h is the height, g is acceleration due to gravity (approximately 9.81 m/s^2) and t is time. Solving this equation for time gives t = sqrt(2h/g) which is roughly 4.16 seconds.

Now considering horizontal motion, the horizontal velocity remains constant at 18 m/s. We can substitute the time obtained from the vertical motion into the equation for horizontal motion to find the horizontal distance the car will travel. Hence, D = V * t = 18 m/s * 4.16 s which is approximately 75 meters. Therefore, the car lands 75.0 meters from the base of the cliff which is option D).