Paper 4, Section I, A

Dynamics and Relativity | Part IA, 2017

A tennis ball of mass mm is projected vertically upwards with initial speed u0u_{0} and reaches its highest point at time TT. In addition to uniform gravity, the ball experiences air resistance, which produces a frictional force of magnitude αv\alpha v, where vv is the ball's speed and α\alpha is a positive constant. Show by dimensional analysis that TT can be written in the form

T=mαf(λ)T=\frac{m}{\alpha} f(\lambda)

for some function ff of a dimensionless quantity λ\lambda.

Use the equation of motion of the ball to find f(λ)f(\lambda).

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