Question

The fastest recorded pitch in Major League Baseball was thrown by Nolan Ryan in 1974. If this pitch were thrown horizontally, the ball would fall 0.809 m (2.65 ft) by the time it reached home plate, 18.3 m (60 ft) away. The acceleration of gravity is 9.81 m/s 2 . How fast was Ryan’s pitch? Answer in units of m/s.

Answer 1

45.06053 m/s

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

g = Acceleration due to gravity = 9.81 m/s²

a = Acceleration

`s=ut+(1)/(2)at^2\\\Rightarrow 0.809=0t+(1)/(2)* 9.81* t^2\\\Rightarrow t=\sqrt{(0.809* 2)/(9.81)}\\\Rightarrow t=0.406\ s`

Time taken by the ball in the horizontal plane

Time = Distance / Speed

`t=(18.3)/(u)`

`s=(1)/(2)gt^2\\\Rightarrow 18.3=(1)/(2)* 9.81* \left((18.3)/(u)\right)^2\\\Rightarrow u=\sqrt{(1)/(2)* 9.81* (18.3^2)/(0.809)}\\\Rightarrow u=45.06053\ m/s`

The Speed of the ball was 45.06053 m/s