Question

A 45-kg football player is running at 7 m/s when he collides with a 55-kg player at rest. Their bodies get tied up after the collision, and they slide across the field at the same speed. What speed are they moving right after the collision?

A) 3.15 m/s
B) 3.85 m/s
C) 5.7 m/s
D) 8.6 m/s

Answer 1

Using the law of conservation of momentum and given that there are no external forces, the combined speed of the players after the collision is 3.15 m/s.

Step-by-step explanation:

To solve for the speed of the players just after the collision, we will use the law of conservation of momentum. The total momentum before the collision must equal the total momentum after the collision since there are no external forces acting on the system.

Let m1 = 45 kg (mass of the first player), v1 = 7 m/s (velocity of the first player), m2 = 55 kg (mass of the second player), and v2 = 0 m/s (velocity of the second player at rest).

Before the collision, the total momentum p is the sum of the individual momenta of both players:

p = (m1 * v1) + (m2 * v2) = (45 kg * 7 m/s) + (55 kg * 0 m/s) = 315 kg·m/s.

After the collision, the players stick together, so their combined mass m_total is m1 + m2 = 100 kg. The total momentum after the collision is m_total * v_final, where v_final is the final velocity of the players together.

Using conservation of momentum:

p = m_total * v_final

315 kg·m/s = 100 kg * v_final

Therefore, v_final = 3.15 m/s.

The players are moving at a speed of 3.15 m/s right after the collision, which corresponds to option A.