Question

Wanting to extend the baseball season into winter, two players decide to practice on some frictionless ice. One player with a mass of 50 kg, initially motionless, catches a 150 g ball moving horizontally at 40 m/s.

A) If the ball sticks in his glove, what will his velocity be after the catch?

B) State whether the collision is elastic or inelastic, and prove it by comparing the energy of the system before and after the catch.

Answer 1

A)

m₁ = mass of first player = 50 kg

v_1i = initial velocity of first player before catching the ball = 0 m/s

m₂ = mass of the ball player = 150 g = 0.15 kg

v_2i = initial velocity of ball just before catching = 40 m/s

V = final velcity of the player-ball combination after catching

using conservation of momentum

m₁ v_1i + m₂ v_2i = (m₁ + m₂) V

(50 x 0) + (0.15 x 40) = (50 + 0.15) V

V = 0.12 m/s in the direction of the ball

b)

the collision is inelastic since the two colliding bodies stick to each other after collision.

KE_f = final total kinetic energy of the system = (0.5) (m₁ + m₂) V² = (0.5) (50 + 0.15) (0.12)² = 0.36 J

KE_i = initial total kinetic energy of the system = (0.5) m₁ v²_1i + (0.5) m₂ v²_2i = (0.5) (50) (0)² + (0.5) (0.15) (40)² = 120 J

since KE_f < KE_i

hence the collision is inelastic