Answer to Question #101792 in Mechanics | Relativity for Alice

Question

A baseball batter swings a 1.54 kg bat at a 356 g ball traveling at 48.7 m/s and the ball is hit 486 ft over the center field wall in 3.6 s. What is the velocity of the bat?

Answer 1

We have:

$$h=v_yt-0.5gt^2$$

$$486(0.3048)=v_y(3.6)-0.5(9.8)(3.6)^2\to v_y=58.8\frac{m}{s}$$

From the conservation of momentum:

$$mv_y=Mu_y\to (0.356)(58.8)=(1.54)u_y$$

Thus, the velocity of the bat:

$$u_x=2v_x=2(48.7)=97.4\frac{m}{s}$$

$$u_y=13.6\frac{m}{s}$$