Question

the fastest tennis service by a man is 246,2 km.hr-1 by Andy Roddick of the United States of America during a match in London in 2004. Calculate the ball's momentum if it has a mass of 58 g?

Answer 1

Approximately
`3.967\; {\rm kg\cdot m\cdot s^(-1)}`.

Step-by-step explanation:

Convert velocity to the standard units (meters per second):

`\begin{aligned}v &= 246.2 \; {\rm km \cdot h^(-1)} \\ &= 246.2 \; {\rm km \cdot h^(-1)}* \frac{1\; {\rm h}}{3600\; {\rm s}} * \frac{1000\; {\rm m}}{1\; {\rm km}} \\ &\approx 68.389\; {\rm m\cdot s^(-1)}\end{aligned}`.

Convert mass to standard units (kilograms):

`\begin{aligned} m &= 58\; {\rm g} \\ &= 58\; {\rm g} *\frac{1\; {\rm kg}}{1000\; {\rm g}}\\ &= 0.058\; {\rm kg}\end{aligned}`.

When an object of mass
`m` travels at a velocity of
`v`, momentum of that object would be
`p = m\, v`. In standard units, the momentum of this tennis ball would be:

`\begin{aligned}p &= m\, v \\ &\approx (0.058\; {\rm kg})\, (68.389\; {\rm m\cdot s^(-1)}) \\ &\approx 3.967\; {\rm kg \cdot m\cdot s^(-1)}\end{aligned}`.