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

Answer:

45.06053 m/s

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

g = Acceleration due to gravity = 9.81 m/s²

a = Acceleration

$s=ut+\frac{1}{2}at^2\\\Rightarrow 0.809=0t+\frac{1}{2}\times 9.81\times t^2\\\Rightarrow t=\sqrt{\frac{0.809\times 2}{9.81}}\\\Rightarrow t=0.406\ s$

Time taken by the ball in the horizontal plane

Time = Distance / Speed

$t=\frac{18.3}{u}$

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

The Speed of the ball was 45.06053 m/s