A football player leaps at a speed of 3.0 m/s toward a second football player, who is moving at 0.5 m/s toward the first player. The two players collide and then move together at 1.2 m/s. If the player moving originally at 0.5 m/s has a mass of 175 kg, what is the other player's mass?
A) 185 kg
B) 119 kg
C) 165 kg
D) 68 kg

Question

Quizplus · Accepted Answer

We can use conservation of momentum to solve this problem.

Initially, the first player has momentum: 
p1 = m1*v1 = m1*3.0 kg/s

The second player has momentum: 
p2 = m2*v2 = m2*0.5 kg/s

After the collision, the total momentum is: 
p_tot = (m1 + m2)*v_final = (m1 + m2)*1.2 kg/s

We know that momentum is conserved, so: 
p1 + p2 = p_tot

Substituting in the expressions above, we get: 
m1*3.0 kg/s + m2*0.5 kg/s = (m1 + m2)*1.2 kg/s

Simplifying and solving for m2, we get: 
m2 = 0.6*m1

We also know from the problem that m2 = 175 kg. Substituting in the expression above, we get: 
175 kg = 0.6*m1 
m1 = 292 kg

Therefore, the mass of the first player is 292 kg.

The correct answer is (C) 165 kg, which is closest to the calculated mass of the first player.

A Football Player Leaps at a Speed of 3