# A projectile is launched with a momentum of 200 kgm/s and 1000 J of kinetic energy. What is the...

## Question:

A projectile is launched with a momentum of 200 kg{eq}\cdot {/eq}m/s and 1000 J of kinetic energy. What is the mass of the projectile?

## Mass of Projectile:

The formulas for kinetic energy K and momentum P of a projectile that we are going to use to compute the required values of the mass of a projectile are shown below:

{eq}\displaystyle K=\frac{1}{2}mv^2\\ \displaystyle P=mv, {/eq} where

• m shows the value of the mass of the projectile.
• v shows the speed of the projectile.

## Answer and Explanation:

Given data:

• The momentum of the projectile is {eq}P=\rm 200\ kg\cdot m/s {/eq}.
• The value of kinetic energy of the projectile is {eq}K=\rm 1000\ J {/eq}.

Here, we have:

{eq}\displaystyle K=\frac{1}{2}mv^2 {/eq}

Multiplying the right-hand side of the above expression by the fraction {eq}\frac{m}{m} {/eq} and simplifying it, we get:

{eq}\begin{align*} \displaystyle K&=\frac{1}{2}mv^2\times \frac{m}{m}\\ \displaystyle K&=\frac{1}{2m}m^2v^2\\ \displaystyle K&=\frac{1}{2m}(mv)^2\\ \displaystyle K&=\frac{1}{2m}(P)^2&\because P=mv\\ \end{align*} {/eq}

Plugging the given values of kinetic energy and momentum of a projectile into the above expression and simplifying it, we have:

{eq}\begin{align*} \displaystyle \rm 1000\ J&=\frac{1}{2m}(\rm 200\ kg\cdot m/s)^2\\ \displaystyle \rm 1000\ J&=\frac{1}{2m}(\rm 40000\ kg^2\cdot m^2/s^2)\\ \displaystyle m&=\rm\frac{1}{2 \times 1000}(\rm 40000)\ kg\\ &=\boxed{\rm 20\ kg}\\ \end{align*} {/eq}

Thus, the mass of the projectile is {eq}20 {/eq} kilograms.