Stunt Car Jump Calculation: How Far Does the Car Land from the Base of the Cliff?

Question:

A stunt man drives a car at a speed of 20m/s off a 30-m-high cliff. The road leading to the cliff is inclined upward at an angle of 20 degrees. How far from the base of the cliff does the car land?

Answer:

The car lands at a distance of 60 m from the base of the cliff.

When solving for the distance the car lands from the base of the cliff, we need to consider the horizontal and vertical components of the car's motion. The initial velocity of the car is 20 m/s and the vertical displacement is 30 m with an angle of 20 degrees.

First, we resolve the velocity into its horizontal and vertical components. Utilizing trigonometry, we find the vertical component to be -6.84 m/s. Considering only the vertical motion and using the kinematic equation for displacement, we calculate that the car lands in 3.2 seconds.

Next, we determine the distance in the horizontal direction using the horizontal component of velocity. Through calculations, we find that the car lands at a distance of 60 meters from the base of the cliff.

By understanding the motion and components involved in the stunt car jump, we can accurately calculate the landing distance of the car. This application of physics principles provides valuable insights into real-world scenarios involving motion and displacement.