Question

question 11. baseball pitchers can throw baseballs up to 45 m/s. a catcher behind home plate often catches the high - speed balls. during the collision of a 0.15 - kg ball and a 1 - kg catchers mitt, the ball exerts a large impulsive force on the catchers mitt. assuming that the total impulse exerted on the mitt cannot be changed, how can the catcher reduce the magnitude of the impulsive force? select all that apply.
a. if the catchers mitt moves toward the ball with a velocity in the opposite direction as the ball as the player makes the catch, the impulsive force will decrease.
b. if the catchers mitt moves with a velocity in the same direction as the ball is moving as the player makes the catch, the impulsive force will decrease.
c. if the catchers mitt has additional padding to increase the time interval during which the mitt experiences the impulsive force, the impulsive force will decrease.
d. if the catchers mitt has a reduced amount of padding to decrease the time interval during which the mitt experiences the impulsive force, the impulsive force will decrease.
e. if the catchers mitt has additional mass, the impulsive force on the mitt will decrease as the momentum of the mitt increases.

Explanation:

Step1: Analyze Impulse - Force Relationship

Impulse \(J = F_{avg}\Delta t\). If the catcher moves the mitt in the opposite direction of the ball (Option A), it increases the time interval \(\Delta t\) over which the force is applied. Since \(J\) (impulse, related to change in momentum) is constant (assuming total impulse is fixed as per the problem), from \(F_{avg}=\frac{J}{\Delta t}\), a larger \(\Delta t\) means a smaller \(F_{avg}\).

Step2: Analyze Padding and Time Interval

If the catcher's mitt has additional padding (Option C), it also increases the time interval \(\Delta t\) during the collision. Using \(F_{avg}=\frac{J}{\Delta t}\) again, with \(J\) constant, a larger \(\Delta t\) leads to a smaller \(F_{avg}\).

Step3: Analyze Option B

If the catcher's mitt moves with the ball (Option B), it is similar to Option A. It increases the time of contact \(\Delta t\). By \(F_{avg}=\frac{J}{\Delta t}\), the impulsive force \(F_{avg}\) will decrease.

Step4: Analyze Option D

Reduced padding (Option D) would decrease the time of contact \(\Delta t\). Using \(F_{avg}=\frac{J}{\Delta t}\), this would increase the impulsive force, so Option D is incorrect.

Step5: Analyze Option E

Increasing the mass of the mitt (Option E) does not directly affect the impulsive force formula \(F_{avg}=\frac{J}{\Delta t}\). The impulsive force is related to the change in momentum of the ball (which determines \(J\)) and the time of contact \(\Delta t\), not the mass of the mitt (as long as we are considering the force on the mitt from the ball, and using the ball's momentum change for impulse calculation). So Option E is incorrect.

Answer:

A. If the catcher’s mitt moves toward the ball with a velocity in the opposite direction as the ball as the player makes the catch, the impulsive force will decrease.
B. If the catcher’s mitt moves with a velocity in the same direction as the ball is moving as the player makes the catch, the impulsive force will decrease.
C. If the catcher’s mitt has additional padding to increase the time interval during which the mitt experiences the impulsive force, the impulsive force will decrease.