Question

A motocross rider at the peak of his jump has a speed such that his centripetal acceleration is equal to g. As a result, he does not feel any supporting force from the seat of his bike, which is also accelerating at rate g. Therefore, he feels if there is no force of gravity on him, a condition described as apparent weightlessness. If the radius of the approximately circular jump is 75.0 m, what is the speed of the bike? (27 m/s)​

Answer 1

The speed of the bike at the peak of the jump to achieve apparent weightlessness is found by equating the centripetal acceleration to the gravitational acceleration, which is approximately 27 meters per second.

To determine the speed of the bike in a motocross jump where the rider experiences apparent weightlessness, we can equate the centripetal acceleration to the acceleration due to gravity (g). The formula for centripetal acceleration (ac) is
`ac = v^2/r,` where v is the speed and r is the radius of the circular path. Given that ac = g, and r = 75.0 m, we can solve for v.

Solving for v, we get:

v = √(g&r)

v = √(9.8 m/s² × 75.0 m)

v ≈ 27 m/s

Therefore, the speed of the bike is approximately 27 meters per second at the peak of the jump to achieve centripetal acceleration equal to the gravitational acceleration.