A baseball comes off the bat with a muzzle velocity of 125.5 mi/hr at an initial

Question

A baseball comes off the bat with a muzzle velocity of 125.5 mi/hr at an initial angle of 45. Take the drag coefficient to be approximately 0.40 for a baseball (the stitches on the baseball actually decrease the drag coefficient from its value of 0.50 for a perfectly smooth sphere). The mass of a baseball is 5.125 oz and the circumference is 9.125 in. Use 1.20 kg/m3 for the density of air. How far does the baseball travel horizontally before hitting the ground? Assume the ball is hit at ground level.

Assuming no air resistance, what is the horizontal range of the ball?

Assuming no air resistance, what is the total time the ball is in the air?

Assuming no air resistance, what is the maximum height reached by the ball?

Assuming no air resistance, how much time does it take for the ball to reach its maximum height?

Assuming no air resistance, what is the speed of the ball at the instant before it hits the ground?

Assuming no air resistance, at what angle does the trajectory of the ball make with respect to the horizontal at the instant before it hits the ground? Since the ball is on its way down, this number should be negative.

Explanation / Answer

Here , for the ball

initial velocity , u = 125.5 mi/hr

u = 56.1 m/s

theta = 45 degree

horizontal range of the ball = u^2 * sin(2*theta)/g

horizontal range of the ball = 56.1^2 * sin(2 * 45 degree)/9.8

horizontal range of the ball = 321 m

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total time the ball is in air = 2 * u * sin(theta)/g

total time the ball is in air = 2 * 56.1 * sin(45 degree)/9.8

total time the ball is in air = 8.1 s

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maximum height reached by the ball = u^2 * sin^2(theta)/(2g)

maximum height reached by the ball = 56.1^2 * sin^2(45 degree)/(2 * 9.8)

maximum height reached by the ball = 80.1 m

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time taken for ball to reach maximum height = total time/2

time taken for ball to reach maximum height = 8.1/2

time taken for ball to reach maximum height = 4.05 s

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speed of ball when it hits ground = initial speed of ball

speed of ball when it hits ground = 56.1 m/s

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the angle will be same , just below the horizontal

final angle made by the ball is -45 degree with the horizontal

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