Question

A pitcher can throw a baseball at about 90 miles/hour (about 39.6 m/s). What is the ratio of the kinetic energy to the rest energy mc2? (Can you use K approximately equals 1/2mv2?)

Answer 1

Answer:

$8.71*10^{-15}$

Explanation:

The rest energy is the energy associated with the base ball at zero velocity which is expressed as

$Rest energy=mc^{2}$

Note: the speed C is the speed of light which is expressed as 3*10^8

while the kinetic energy is the energy associated with the ball during its motion and is expressed as

$Kinetic energy=1/2mv^{2}$

the ratio can be expressed as

$\frac{Kinetic Energy}{Rest Energy}=\frac{\frac{1}{2}mv^{2} }{mc^{2}}\\since V=39.6m/s\\C=3*10^{8}m/s\\\frac{Kinetic Energy}{Rest Energy}=\frac{\frac{1}{2}39.6^{2} }{(3*10^8)^{2}} \\\frac{Kinetic Energy}{Rest Energy}=\frac{784.08}{9*10^{16}} \\\frac{Kinetic Energy}{Rest Energy}=8.71*10^{-15}$