A pitcher claims he can throw a 0.147-kg baseball with as much momentum as a 3.5

Question

A pitcher claims he can throw a 0.147-kg baseball with as much momentum as a 3.50-g bullet moving with a speed of 1.50 103 m/s. What must the baseball's speed be if the pitcher's claim is valid? Which has greater kinetic energy, the ball or the bullet?

A pitcher claims he can throw a 0.147-kg baseball with as much momentum as a 3.50-g bullet moving with a speed of 1.50 x 10 m/s (a) What must the baseball's speed be if the pitcher's claim is valid? m/s (b) Which has greater kinetic energy, the ball or the bullet? The bullet has greater kinetic energy. The ball has greater kinetic energy Both have the same kinetic energy.

Explanation / Answer

Given that the mass of base ball is m1 = 0.147 kg

Mass of bullet is m2 = 3.5g = 3.5x10^-3 kg

speed of bullet is v2 = 1.50x10^3 m/s

(a) Since the both ball and bullet having same momentum

                       m1 x v1 = m2 x v2

v1 = (m2 x v2) / m1 = (3.5x10^-3 kg) (1.50x10^3 m/s) / 0.147 kg = 35.71 m/s

(b) The kinetic energy of the body related to the momentum as

                         KE = (momentum)^2 / 2m

     From the above equations it is clear that the kinetic energy inversely praportional to the mass of the body.

     So the kinetic energy is greater for the lower mass of the body for same momentum.

     Thus the kinetic energy of bullet greater than the base ball.

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