How long is the ball in the air during this interval?

While at bat a 5′10′′ baseball player hits a homerun. To do this the player swings the bat at a height of half his body height. The ball leaves the bat at a speed of 115mph at an angle of 81° from the vertical. The ball just skims the top of the 9ft outfield wall as it leaves the park.

a. Make a complete set of position, velocity, and acceleration motion graphs describing the ball between the hit and the instant when it goes over the wall and label the important features. Assume that 𝑡 = 0 the moment the ball is hit, up is positive, the ball moves in the positive horizontal direction, and that the pitcher’s mound (60’ from home plate, neglect its height) is the coordinate origin.

b. How long is the ball in the air during this interval?

c. How far away from home plate is the outfield wall?

d. Based on the numbers given and your answers, what might an average spectator (a non-physicist) say about this somewhat unusual homerun? Explain why you think so. You may look up helpful data about the game of baseball for this.

e. What angle relative to +𝑥-axis is the ball moving at when it passes over the wall?

f. If an infield player can jump high enough to just get his mitt 9ft off the ground, what is the furthest he can catch the ball before it gets to the his teammate at the outfield wall?

g. How much time will the infielder have to react to and catch the ball?

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