A golf ball of mass 0.05 kg is struck by a golf club of mass m kg with a speed of 50m/s will have an initial speed of v(m)=83m/(m+0.05) m/s. show that v'(m)0 and interpret this result in context with the application. Compare v'(0.15) and v'(0.20) in context of the application as well.

Question

A golf ball of mass 0.05 kg is struck by a golf club of mass m kg with a speed of 50m/s will have an initial speed of v(m)=83m/(m+0.05) m/s. show that v'(m)>0 and interpret this result in context with the application. Compare v'(0.15) and v'(0.20) in context of the application as well.

Steve · Accepted Answer

v(m) = 83m / (m+0.05)
dv/dm = 1660/(20x+1)^2 = 4.15/(x+0.05)^2

clearly v' > 0

v(m) = 83 - 83/(20m+1)

clearly the maximum possible initial velocity is 83m/s, which is achievable only with a golf club of infinite mass.

naturally, a heavier club hits the ball faster