Question

" A ball with a velocity of 7 m/s collided with a 2nd ball with a mass of 2 kg. The first ball stops and the 2nd ball is launched forward with a velocity of 9 m/s. What is the mass of the first ball?

a) 3 kg
b) 5 kg
c) 7 kg
d) 14 kg"

Answer 1

Using conservation of momentum, the mass of the first ball is calculated to be approximately 2.57 kg, which does not match any of the provided answer choices, indicating an error in the question or the options.

Step-by-step explanation:

The mass of the first ball can be determined using the principle of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after a collision, provided no external forces are acting on the system. The momentum of an object is given by the product of its mass and velocity (p = m * v).

Let's denote the mass of the first ball as m1 and its initial velocity as v1. The second ball has a mass m2 of 2 kg and its velocity after collision is v2' of 9 m/s. The first ball comes to a stop, so its velocity after collision v1' is 0 m/s. Since the first ball stops after the collision, all its momentum is transferred to the second ball.

Applying the conservation of momentum:

• Before collision: total momentum = m1 * v1 + m2 * v2 (where v2 is 0 because the second ball is at rest)
• After collision: total momentum = m1 * v1' + m2 * v2' (where v1' is 0 because the first ball stops)

Therefore, the equation simplifies to:

m1 * v1 = m2 * v2'

Now we can solve for m1:

m1 = (m2 * v2') / v1

m1 = (2 kg * 9 m/s) / 7 m/s

m1 = 18/7 kg

m1 ≈ 2.57 kg

This result does not match any of the given options, indicating a possible mistake in either the question or the provided multiple-choice answers. Therefore, based on the information presented, no answer from the given options is correct.