A 0.01-kg baseball traveling in a horizontal direction with a speed of 11 m/s hits a bat and is popped straight up with a speed of 15 m/s.
(a) What is the change in momentum (magnitude and direction) of the baseball?
They already told you that the direction change is 90 degrees, from horizontal to "up". Use the Pythagorean Theorem for the magnitude.
To find the change in momentum of the baseball, you need to determine the initial momentum and final momentum, and then calculate the difference between the two.
1. Find the initial momentum:
The initial momentum (p_initial) of an object is given by the formula: p_initial = mass × velocity.
In this case, the mass of the baseball is 0.01 kg, and its initial speed is 11 m/s. Therefore, the initial momentum is:
p_initial = 0.01 kg × 11 m/s = 0.11 kg·m/s.
2. Find the final momentum:
The final momentum (p_final) is calculated in the same way, using the mass and speed after the collision. Since the baseball is popped straight up, its horizontal speed does not matter. So, we only need to consider its vertical speed, which is 15 m/s.
Therefore, the final momentum is:
p_final = 0.01 kg × 15 m/s = 0.15 kg·m/s.
3. Calculate the change in momentum:
The change in momentum Δp is given by the formula: Δp = p_final - p_initial.
Substituting the values we found earlier, we have:
Δp = 0.15 kg·m/s - 0.11 kg·m/s = 0.04 kg·m/s.
The magnitude of the change in momentum is 0.04 kg·m/s, and its direction is determined by the subtractive operation between final and initial momenta. Since p_final is greater than p_initial, the direction of the change in momentum is upward.