Question

Einstein and Lorentz, being avid tennis players, play a fast-paced game on a court where they stand 20.0 m from each other. Being very skilled players, they play without a net. The tennis ball has mass 0.0580 kg. You can ignore gravity and assume that the ball travels parallel to the ground as it travels between the two players. Unless otherwise specified, all measurements are made by the two men.

(a) Lorentz serves the ball at 80.0 m/s. What is the ball's kinetic energy?
(b) Einstein slams a return at 1.80 x 10^8 m/s. What is the ball's kinetic energy?

Answer 1

Step-by-step explanation:

a ) Kinetic energy of ball = 1/2 m v² , m is mass of the ball and v is its velocity

= 1/2 x .058 x 80²

= 185.6 J .

b ) The velocity of ball is very high so we shall find out the relativistic kinetic energy , the formula is given below

kinetic energy = mc² (
`\frac{1}{\sqrt{1-(v^2)/(c^2) } } -1` )

= mc² x
`\frac{1}{\sqrt{1-(v^2)/(c^2) } }` - mc²

= .058 x 9 x 10¹⁶ x
`\frac{1}{\sqrt{1-(1.8^2)/(3^2) } }` - .058 x 9 x 10¹⁶

= .058 x 9 x 10¹⁶ x 1 / .8 - .058 x 9 x 10¹⁶

.058 x 9 x 10¹⁶ ( 1.25 - 1 )

= .058 x 9 x 10¹⁶ x .25

= .1305 x 10¹⁶

= 13.05 x 10¹⁴ J .