Question

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?

Answer 1

The mass of the toy dart is `"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 `color(red)(rho=m*v)`, where `rho`, (pronounced "roe") is momentum, `m` is mass, and `v` is velocity.

Known
`rho=0.180color(white)(.)"kg"*"m/s"`

`v="4.1 m/s"`

Unknown
`m=???`

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

`color(red)(m=rho/v)`

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