webassign requests answer in meters: Ted Williams hits a baseball with an initia

Question

webassign requests answer in meters:

Ted Williams hits a baseball with an initial velocity of 120 miles per hour (176 ft/s) at an angle of ? = 35 degrees to the horizontal. The ball is struck 3 feet above home plate. You watch as the ball goes over the outfield wall 420 feet away and lands in the bleachers. After you congratulate Ted on his hit he tells you, 'You think that was something, if there was no air resistance I could have hit that ball clear out of the stadium!'

Assuming Ted is correct, what is the maximum height of the stadium at its back wall x = 565 feet from home plate, such that the ball would just pass over it?
You may need:
9.8 m/s2 = 32.2 ft/s2
1 mile = 5280 ft
h =

Explanation / Answer

taking all the values in a FPS system

now the horizontal and vertical positions , and accelerations
  

horizontal component of position as a function of time and vx is

   x = 176*Cos(35 )*t = 144.17 t

given it will cover horizontal distance is 565 ft so time taken is t = 565/144.17= 3.92 s

now vertical component of the ball is

   y = y0 +u sin theta*t- 1/2 at^2
          = 3+176 Sin 35 *t - 16.1*t^2
          = 3+395 - 15.34
          = 150.6 feet
the can reach a height of 150.6 feet

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