baseball Ted Williams hits a baseball with an initial velocity of 120 miles per
ID: 1807077 • Letter: B
Question
baseball 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
Solution:-
The horizontal component of position is a function only of time and horizontal velocity.
x = 176*cos(35°)*t
x = 144.171*t
The ball will cover the horizontal distance of 565 feet in time
t = 565/144.171
= 4.12705 seconds
The vertical component of position is a function of the initial ball height, its vertical velocity, and the acceleration due to gravity.
y = 3 + 176*sin(35°)*t - 16t2
Evaluated at the above time, the ball has height
y = (-16*4.12705 + 100.949)*4.12705 + 3
y = 147.1 feet
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