A softball is hit over a third baseman\'s head with some speed v 0 at an angle ?

Question

A softball is hit over a third baseman's head with some speed v0 at an angle ? above the horizontal. Immediately after the ball is hit, the third baseman turns around and begins to run at a constant velocity V=7.00m/s. He catches the ball  t=2.00s later at the same height at which it left the bat. The third baseman was originally standing L=18.0m from the location at which the ball was hit.

Part A) Find v0. Use g=9.81m/s2 for the magnitude of the acceleration due to gravity. Vo=? in m/s

Part B) Find the angle ? in degrees.

A softball is hit over a third baseman's head with some speed v0 at an angle ? above the horizontal. Immediately after the ball is hit, the third baseman turns around and begins to run at a constant velocity V=7.00m/s. He catches the ball t=2.00s later at the same height at which it left the bat. The third baseman was originally standing L=18.0m from the location at which the ball was hit. Find v0. Use g=9.81m/s2 for the magnitude of the acceleration due to gravity. Vo=? in m/s Find the angle ? in degrees.

Explanation / Answer

time of flight = 2 sec

Range = 18 + 7 x 2 = 32 m

in vertical : H = ut + at^2/2

0 = vosintheta x 2 - g x 2^2/2

vo x sin(theta) = 9.81 ..(i)

on horizontal : vocos(theta) x 2 = 32

vo x cos(theta) = 16   ..(ii)

(i) / (ii)   = tan(theta) = 9.81/16

theta   = 31.51 degrees    ........................Ans. (Part B)  

vo = 16 /cos31.51 = 18.77 m/s ...........ANs.PartA

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