A batter hits a fly ball which leaves his bat a distance of 0.90 m above the gro

Question

A batter hits a fly ball which leaves his bat a distance of 0.90 m above the ground at an angle of 61 from horizontal and an initial speed of 28 m/s toward center field. Ignore air effects.

1- how far from home plate would the ball land if not caught?

2-the ball is caught by a centerfielder who started at a distance of 105 m from home plate and who at the same time the ball was hit, runs straight toward home plate and dives to make a catch as the ball reaches ground level. Find the fielder's average speed.

Explanation / Answer

Ok, lets consider the vertical motion of the ball from its start till it reaches its highest point.
At the highest point, the vertical velocity = 0 and the time taken is half the original time for the ball to hit the ground.
Using the simple equations of motion, v = u +at
here v = 0, u = 28 (sin 61), a = -9.81
hence t = 2.5 s,
but the time to hit the ground would be 5 s

Now considering the horizontal motion of the ball, and using another equation of motion s = ut + 0.5 at^2

in its horizontal motion, a the acceleration = 0,
therefore the distance, s = ut, where u = 28 (cos) 61 and t = 5

it follows that s = 67.87 m



as for the fielders speed, the time taken is 5 seconds and he runs 105 m, since average speed, v = distance/time

v = 105/5 = 21 m/s

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