Exciting Stunt Driver Challenge: Jumping Over Cars!

Challenge:

Imagine a stunt driver aiming to jump over 8 cars parked side by side below a horizontal ramp with a vertical height of 1.5 m and a horizontal distance to clear of 22 m.

1. What is the minimum speed required when the ramp is level?

2. What is the new minimum speed needed if the ramp is tilted upward, creating a "takeoff angle" of 7.0∘ above the horizontal?

Answers:

1. The minimum speed required when the ramp is level is approximately 10.6 m/s.

2. The new minimum speed needed with the ramp tilted upward is approximately 11.6 m/s.

Explanation:

To calculate the minimum speed required for the stunt driver to jump over the 8 cars, we can use the principles of projectile motion.

When the ramp is level, the minimum speed can be calculated using the equation for range:

Range = (velocity^2 * sin(2θ)) / g

Substituting the given values, the minimum speed required is approximately 10.6 m/s.

When the ramp is tilted upward with a takeoff angle of 7.0∘, the minimum speed needed to clear the same horizontal distance can be found using the equation:

v = √((d * g) / (cos(θ) * sin(θ)))

Substituting the given values, the new minimum speed required is approximately 11.6 m/s.

By understanding the physics behind projectile motion and the effects of ramp angles, the stunt driver can successfully perform the exhilarating jump over the cars!