9. In the sun devil football game, a receiver, who is standing still, has caught a pass from the quarterback. Before he can move, a tackler, running at a velocity of + 6.89 m/s, grabs him. The tackler holds onto the receiver, and the two head off with a velocity of + 4.78 m/s. The mass of the tackler is 156 kg. Ignoring any frictional forces, what is the mass of the receiver?

The mass of the receiver is 68.862 kg

Explanation:

Given;

let mass of the receiver be "m₁"

initial velocity of the receiver, u₁ = 0

mass of the tackler, m₂ = 156 kg

initial velocity of the tackler, u₂ = 6.89 m/s

their final velocity, v = 4.78 m/s

Apply the principle of conservation of linear momentum, for inelastic collision;

m₁u₁ + m₂u₂ = v (m₁ + m₂)

(m₁ x 0) + (156 x 6.89) = 4.78 (m₁ + 156)

0 + 1074.84 = 4.78 (m₁ + 156)

1074.84 = 4.78 (m₁ + 156)

m₁ + 156 = 1074.84 / 4.78

m₁ + 156 = 224.862

m₁ = 224.862 - 156

m₁ = 68.862 kg

Therefore, the mass of the receiver is 68.862 kg