Find the direction and magnitude of the impulse

[dg_5021]

A .14 kg baseball moves toward home plate with a velocity vi=-36 m/s x. After striking the bat moves vertically upward with a velocity vf= 18 m/s y. (a) Find the direction and magnitude of the impulse delivered to the ball by the bat. Assume that the ball and bat are in contact for 1.5ms. (b) How would your answer to part (a) change if the mass of the ball were doubled? (c) How would your answer to part (a) change if the mass of the bat were doubled?

how do u do this problem am so confused? This is what i came up with so far
((36)^2+(18)^2)^(1/2)= 40.2492
tan^-1(18/36)= 26.5651
i don't know what to do from there?

 

[Doc Al]

The impulse equals the change in momentum of the ball. Assuming the given initial and final velocities are the same, how does the mass of the ball or bat affect the momentum of the ball?

 

[wais]

To solve this problem, we can use the equation for impulse: J = mΔv, where J is the impulse, m is the mass, and Δv is the change in velocity. We also know that impulse is a vector quantity, meaning it has both magnitude and direction.

(a) To find the direction of the impulse, we can use the fact that the initial velocity of the ball is in the negative x-direction and the final velocity is in the positive y-direction. This means that the impulse is in the direction of the y-axis, or vertically upward. To find the magnitude of the impulse, we can plug in the given values into the equation for impulse:

J = (0.14 kg)(18 m/s - (-36 m/s)) = 7.56 Ns

(b) If the mass of the ball were doubled, the magnitude of the impulse would also double, since the mass is directly proportional to the impulse. The direction of the impulse would remain the same, as it is determined by the change in velocity.

(c) If the mass of the bat were doubled, the magnitude of the impulse would also double, since the mass is directly proportional to the impulse. However, the direction of the impulse would change. Since the mass of the bat is now larger, it would have a greater influence on the direction of the impulse. The impulse would now be more in the direction of the x-axis, or horizontally. The exact direction would depend on the specific values of the mass and velocity of the bat.