## Question

While driving in your pickup truck down Highway 280 between San Francisco and Palo Alto, a meteorite lands in your truck bed! Despite its 220 kg mass, the meteor does not destroy your 1200 kg truck.

In fact, it landed so softly it added mass but did not change the total momentum of your truck.

Before the meteor landed you were going 25 m/s. After it landed, approximately how fast were you going? Answer in m/s.

### Answer

The final answer to this question for the final velocity is 21 m/s

#### Explanation

We need to start by extracting our data from the question

**Data**

Our Initial mass which is the mass of the truck is m_{1} = 1,200 kg

The second mass is the mass of the meteorite, m_{2} = 220 kg

Your initial velocity before the meteor landed on the truck is u_{1} = 25 m/s

The velocity after the meteor landed on the truck is u_{2} = 0

The final velocity is v_{1} = v_{2} = v

**Formula**

We will make v subject of the formula from the formula of momentum, which is

m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}

But v_{1} = v_{2} = v

Thus,

m_{1}u_{1} + m_{2}u_{2} = (m_{1} + m_{2})v

At the same time, the velocity (u_{2}) after the meteor landed on the truck is zero (0)

Hence,

m_{1}u_{1} + m_{2} x 0 = (m_{1} + m_{2})v

Which is equal to

m_{1}u_{1} = (m_{1} + m_{2})v

We can now divide both sides by (m_{1} + m_{2}) to obtain

Therefore, **the formula to apply so that we can find the velocity traveled so far of v = m _{1}u_{1} / (m_{1} + m_{2})**

##### Solution

We will now insert our data into the formula **v = m _{1}u_{1} / (m_{1} + m_{2})** to obtain

**v = m _{1}u_{1} / (m_{1} + m_{2})** = (1200 x 25) / (1200 + 220)

Thus,

v = 30,000 / 1420 = 21.126 m/s

**Therefore, after the meteor landed, the speed covered by the truck is approximately 21 meters per second.**

*You may also like to read:*

The Linear Momentum of a Truck of Mass 5000 kg

Newton’s Second Law Practice Problems

Also Newton’s Second Law of Motion Examples