During a baseball game a 65 kg runner is coming towards home plate at a speed of

Question

During a baseball game a 65 kg runner is coming towards home plate at a speed of 6 m/s. This runner must slide into home such that their speed is zero at the instant home plate is touched. The coefficient of kinetic friction between the runner and the ground is 0.75.

a) Determine the energy lost due to friction during the slide.

b) Find the distance of the slide.

c) If instead the runner started the slide later, at a distance half of that found in part b, with what speed would the runner begin slidiing when they reach home?

Explanation / Answer

(a) Conservation of energy

Energy lost = 0.5 m u^2 = 0.5 * 65 * 6^2 = 1170 J

(b) 0.5 m u^2 = k m g d

d = 0.5 u^2 / ( k g) = 0.5 * 6^2 / (0.75*9.81) = 2.44 m

Distance of slide = 2.44 m

(c) 0.5 m u^2 = k m g d / 2 + 0.5 m v^2

v = sqrt( u^2 - k g d ) = sqrt ( 6^2 - 0.75 * 9.81 * 2.44 ) = 4.25 m/s

speed = 4.25 m/s

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