A 50 kg skater at rest on a frictionless rink throws a 2 kg ball, giving the ball a velocity of 10 m/s. Which statement describes the skaters subsequent motion? Explain please.

a. 0.4 m/s in the same direction as the ball.
b. 0.4 m/s in the opposite direction of the ball.
c. 2 m/s in the same direction as the ball.
d. 4 m/s in the same direction as the ball.
e. 4 m/s in the opposite direction of the ball

(b)0.4m/s in the opposite direction of the ball.

How..??

Please explain how,?????...??

When using the equation for conservation of momentum (Pinitial=Pfinal), the equation should always be set up like this: m1v1i-m2v2i=m1v1f-m2v2f). Since both objects are initially at rest, the left side of the equation is equal to zero. m1 represent the mass of the skater and v1f represent their final velocity (which you're solving for). Plug in the mass and the velocity of the ball for m2 and v2f and solve for v1f.

Steps:

0=m1v1f-m2v2f
0=(50kg)(v1f)-(2kg)(10m/s)
v1f=.4m/s

To determine the subsequent motion of the skater, we need to apply the law of conservation of momentum. According to this law, the total momentum of an isolated system remains constant before and after an interaction.

The momentum of an object is given by the product of its mass and velocity. So, we can calculate the momentum of the ball and the skater separately.

Momentum of the ball (before interaction) = mass of the ball * velocity of the ball
Momentum of the ball (before interaction) = 2 kg * 10 m/s = 20 kg·m/s

Since the skater is at rest before throwing the ball, their initial momentum is zero.

Now, considering the conservation of momentum, the total momentum after the interaction must also be zero. This means that the momentum of the skater after throwing the ball must equal the initial momentum of the ball.

Momentum of the skater (after interaction) = 20 kg·m/s

To calculate the velocity of the skater, we divide the momentum by the mass of the skater.

Velocity of the skater (after interaction) = momentum of the skater / mass of the skater
Velocity of the skater (after interaction) = 20 kg·m/s / 50 kg
Velocity of the skater (after interaction) = 0.4 m/s

Therefore, the correct statement is: a. The skater moves with a velocity of 0.4 m/s in the same direction as the ball. This means that the skater moves forward, just like the ball, but at a slower speed.