Question

The fastest recorded pitch in Major League Baseball, thrown by Aroldis Chapman in 2010, was clocked at 169.14 km/h (105.1 mi/h). If a pitch were thrown horizontally with this velocity, what would the ball's vertical displacement be by the time it reached home plate, 18.3 m (60.0 ft) away?

Answer 1

The ball would fall vertically for 112.45m

Step-by-step explanation:

The vertical height of a horizontal throw is affected only by the speed of the throw and the acceleration due to gravity.

At this point, we may use this formula to determine the vertical height of the throw

vertical height =

The initial throwing speed has to be converted to m/s to ensure uniformity during the calculations. To do this we multiply by 1000 and divide by 3600

169.1km/hr = 46.972m/s

Maximum height = m

The pitch would make the ball fall vertically for 112.45m by the time it reached the home plate 18.2 m away

Answer 2

The ball's vertical displacement 5.7 cm

Step-by-step explanation:

Given:

V₀ = 169.14 m

D = 18.3 m

g = 9,81 m/s²

____________

Δh - ?

Ball flight time:

t = D / V₀ = 18.3 / 169.14 ≈ 0.108 s

The ball's vertical displacement:

Δh = g·t² / 2

Δh = 9.81·0.108² / 2 ≈ 0,057 m or 5.7 cm