Question

You are standing on a very slippery icy surface and throw a 1-kg football horizontally at a speed of 6.7 m/s. What is your velocity when you release the football? Assume your mass is 65 kg.

a) 0 m/s
b) 6.7 m/s
c) 9.8 m/s
d) 13.5 m/s

Answer 1

By applying the conservation of momentum, your velocity when releasing a 1-kg football thrown at 6.7 m/s is calculated to be 0.103 m/s, considering your mass of 65 kg. Momentum conservation dictates that your movement will be in the opposite direction to the football's throw.

Step-by-step explanation:

To determine your velocity when you release the football, we will apply the conservation of momentum principle since there are no external forces acting horizontally on the system (you and the football). Before you throw the football, both you and the football are stationary relative to the ground, meaning the initial total momentum of the system is zero. When you throw the football, to conserve momentum, your body will move in the opposite direction.

The momentum of the football when thrown is:

mfootball × vfootball = 1 kg × 6.7 m/s = 6.7 kg·m/s.

Since momentum is conserved and initially was zero, the momentum of your body (myou × vyou) must be equal in magnitude and opposite in direction to the momentum of the football:

65 kg × vyou = -6.7 kg·m/s.

Solving for vyou:

vyou = -6.7 kg·m/s / 65 kg = -0.103 m/s.

Since the question is asking for the magnitude of your velocity, we can ignore the negative sign which indicates direction and just give the magnitude:

Your velocity when you release the football is 0.103 m/s.