Question

A 4000-kg truck traveling with a velocity of 20 m/s due south collides head-on with a 1350-kg car traveling with a velocity of 10 m/s due north. The two vehicles stick together after the collision. What is the momentum of each vehicle prior to the collision?

Answer 1

Answer:Momentum of Truck
`=4000* 20=80,000 kg-m/s`

Momentum of car
`=1350* 10=13,500 kg-m/s`

Step-by-step explanation:

Given

mass of truck(m)=4000 kg

Velocity of Truck is (
`V_T`)=
`-20\hat{j}`

mass of car (
`m_c`)=1350 kg

Velocity of car
`(V_c)=10 \hat{j}`

Conserving momentum

`4000* \left ( -20\right )+1350\left ( 10\right )=5350v`

`v=(66,500)/(5350)=12.42 m/s`

Momentum of Truck
`=4000* 20=80,000 kg-m/s`

Momentum of car
`=1350* 10=13,500 kg-m/s`

Answer 2

1) Momentum of truck before collision is
`\overrightarrow{p_(1)}=-80000kgm/s`

2) Momentum of car before collision is
`\overrightarrow{p_(2)}=13500kgm/s`

Step-by-step explanation:

The momentum of an object with mass 'm' travelling with speed 'v' is mathematically given by

`\overrightarrow{p}=mass* \overrightarrow{v}`

In this problem we shall assume that direction's coincide with the Cartesian axis for simplicity

Thus for Truck we have

Mass = 4000 kg

Velocity =
`-20\widehat{j}`m/s

Thus momentum of truck becomes

`\overrightarrow{p_(1)}=4000* -20\overrightarrow{j}=-80000kgm/s`

Similarly for car we have

Mass = 1350 kg

Velocity =
`10\widehat{j}`m/s

Thus momentum of car becomes

`\overrightarrow{p_(2)}=1350* 10\overrightarrow{j}=13500kgm/s`