Question

a baseball is hit at ground level. the ball is observed to reach its maximum height above ground level 3.0 seconds after being hit. and 2.5 seconds after reaching this maximum height, the ball is observed to barely clear a fence that is 320 ft. from where it was hit. how high is the fence? (the acceleration of gravity is -32.2 ft/s 2 .)

Answer 1

To find the height of the fence, we need to find the final height of the ball after it was hit and then subtract the height of the fence.The final height of the ball can be found using kinematic equations. Using the initial velocity, acceleration due to gravity, and time elapsed, we can find the final height of the ball:h = vi * t + 0.5 * a * t^2whereh = final height

vi = initial velocity (0, since it was hit from ground level)

t = time elapsed (3.0 s)

a = acceleration due to gravity (-32.2 ft/s^2)Substituting the values,h = 0 + 0.5 * -32.2 * (3.0)^2 = 45.3 ftNext, we need to find the height of the ball 2.5 seconds after it reached its maximum height.Using the same kinematic equation,h = vi * t + 0.5 * a * t^2whereh = final height

vi = initial velocity (0, since it was at its maximum height)

t = time elapsed (2.5 s)

a = acceleration due to gravity (-32.2 ft/s^2)Substituting the values,h = 0 + 0.5 * -32.2 * (2.5)^2 = 18.825 ftFinally, subtracting the final height of the ball from the height of the fence:fence height = 320 ft - 18.825 ft = 301.175 ftSo, the fence is 301.175 ft high