Projectile Motion Analysis in Stunt Driving Scenario

What speed must the stunt driver be driving to safely cross a bed of spikes?

How fast must the stunt driver be driving to make it safely across?

Answer:

The stunt driver must drive at an approximate speed of 11.25 m/s to safely cross a 13.5 m wide bed of spikes from a 7.3 m tall platform.

The scenario presented involves a stunt driver driving a motorcycle horizontally off a 7.3m tall platform and attempting to cross a 13.5m wide bed of spikes. To determine the speed required for the stunt driver to safely make it across, we need to apply principles of projectile motion.

Projectile motion is a fundamental concept in physics, particularly in mechanics. It involves the motion of an object projected into the air at an angle or in this case, horizontally. In this scenario, we can treat the horizontal and vertical motions separately.

When focusing on the vertical motion of the motorcycle, we can calculate the time it takes for the bike to fall from the platform using the equation t = sqrt((2h)/g), where h is the height of the platform (7.3m) and g is the acceleration due to gravity (approximately 9.8 m/s²). By solving this equation, we find that the time to fall is approximately 1.2 seconds.

Once we have the time it takes to fall, we can then determine the velocity needed to cover the 13.5m distance in this time. Using the equation v = d/t, where d is the distance (13.5m) and t is the time calculated earlier, we find that the speed required for the stunt driver to safely cross is approximately 11.25 m/s.

Understanding projectile motion is crucial in analyzing scenarios like this stunt driving situation. By applying these principles, we can calculate the necessary speed for the stunt driver to successfully navigate the challenge and land safely on the other side of the bed of spikes.