Question

1. 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 as 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 was the speed of the bike?

Explanation:

Step1: Recall centripetal acceleration formula

The centripetal acceleration formula is \(a_{c}=\frac{v^{2}}{r}\).

Step2: Substitute known values

We know that \(a_{c} = g\) (where \(g = 9.8\ m/s^{2}\)) and \(r=75.0\ m\). Substituting into the formula \(g=\frac{v^{2}}{r}\).

Step3: Solve for \(v\)

Rearrange the formula to solve for \(v\): \(v=\sqrt{gr}\).
Substitute \(g = 9.8\ m/s^{2}\) and \(r = 75.0\ m\) into the formula: \(v=\sqrt{9.8\times75.0}\).
Calculate \(9.8\times75.0 = 735\). Then \(v=\sqrt{735}\approx27.1\ m/s\).

Answer:

The speed of the bike is approximately \(27.1\ m/s\).