Stanton hit the second hardest homerun of the 2014 season with an initial speed

Question

Stanton hit the second hardest homerun of the 2014 season with an initial speed of 120 mph at an angle 20 degrees above the horizontal.

According to data available through ESPN, Stanton’s homerun traveled 428 feet. It’s probably no surprise to you that the atmosphere significantly affects the flight of the ball. It may surprise you how large the effect can be.

Calculate how far Stanton’s homerun would have traveled if the earth had no atmosphere. Assume the ball/bat collision occurred 3 feet above the ground. Give your answer in feet. (The acceleration due to gravity is 32.2 ft/s2).

Explanation / Answer

here ,

initial speed of ball , vi = 120 mph = 176 feet/s

let the distance travelled is x

Using trajectory of projectile

y = y0 + x * tan(theta) - g * x^2/(2 * (vi * cos(theta))^2)

0 = 3 + x * tan(20) - 32.17 * x^2/(2 * (176 * cos(20))^2)

solving for x

x = 627.1 feet

Stanton’s homerun would have traveled 627.1 feet if the earth had no atmosphere.

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