How to Safely Jump Over 8 Parked Cars: A Stunt Driver's Challenge
What minimum speed does a stunt driver need to jump over 8 cars parked side by side below a horizontal ramp?
The stunt driver needs to clear a horizontal distance of 22 m and a vertical height of 1.5 m above the cars. What is the minimum speed required for this daring stunt?
How does the new minimum speed change if the ramp is tilted upward with a 7.0° takeoff angle?
What adjustments need to be made to the minimum speed required when the ramp is tilted upward at a 7.0° angle above the horizontal?
Answer:
To successfully jump over 8 cars parked side by side below a horizontal ramp, the stunt driver needs to have a minimum speed of approximately 23.8 m/s. If the ramp is tilted upward with a takeoff angle of 7.0° above the horizontal, the new minimum speed required will be slightly lower.
Explanation: In order to calculate the minimum speed required for the stunt driver to jump over the 8 cars, we need to consider the horizontal distance and vertical height that must be cleared. The stunt driver will need to clear 22 m horizontally and reach a height of 1.5 m above the cars.
To calculate the minimum speed, we can apply the principles of projectile motion. The horizontal distance traveled can be determined using the equation: range = horizontal velocity × time. The time can be calculated using the equation: time = vertical distance / vertical velocity. The vertical velocity can be calculated using the equation: vertical velocity = √(2 × acceleration due to gravity × vertical distance).
By substituting the given values into these equations, we find that the minimum speed required for the stunt driver is approximately 23.8 m/s.
When the ramp is tilted upward at a 7.0° angle above the horizontal, the takeoff angle affects the vertical and horizontal components of the car's velocity. The horizontal component of the velocity remains the same, while the vertical component is altered by the angle of the ramp.
To find the new minimum speed required with the ramp tilted upward, we can calculate the new vertical component of the velocity using the equation: vertical velocity = horizontal velocity × tan(takeoff angle). By substituting the values into this equation, we determine that the new minimum speed required will be slightly lower than the initial 23.8 m/s.