# A toy dart gun generates a dart with 0.180 kg.m/s momentum and a velocity of 4.1 m/s. What is the mass of the dart in grams rounded to 2 significant figures?

Jan 27, 2017

The mass of the toy dart is $\text{0.044 kg}$ rounded to two significant figures.

#### Explanation:

Momentum is mass in motion. Momentum depends on the mass of the object in motion and its velocity. Because velocity is a vector quantity, momentum is a vector quantity, even though a direction was not included in this question.

The equation for momentum is $\textcolor{red}{\rho = m \cdot v}$, where $\rho$, (pronounced "roe") is momentum, $m$ is mass, and $v$ is velocity.

Known
$\rho = 0.180 \textcolor{w h i t e}{.} \text{kg"*"m/s}$

$v = \text{4.1 m/s}$

Unknown
m=???

Solution
Rearrange the equation for momentum to isolate mass. Substitute the known values into the equation.

$\textcolor{red}{m = \frac{\rho}{v}}$

m=(0.180"kg"*cancel"m/s")/("4.1 "cancel"m/s")="0.044 kg" rounded to two significant figures