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$=4000\times 20=80,000 kg-m/s$

Momentum of car$=1350\times 10=13,500 kg-m/s$

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

$4000\times \left ( -20\right )+1350\left ( 10\right )=5350v$

$v=\frac{66,500}{5350}=12.42 m/s$

Momentum of Truck$=4000\times 20=80,000 kg-m/s$

Momentum of car$=1350\times 10=13,500 kg-m/s$

Answer 2

Answer:

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

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

Explanation:

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

$\overrightarrow{p}=mass\times \overrightarrow{v}$

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

$\overrightarrow{p_{1}}=4000\times -20\overrightarrow{j}=-80000kgm/s$

Similarly for car we have

Mass = 1350 kg

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

Thus momentum of car becomes

$\overrightarrow{p_{2}}=1350\times 10\overrightarrow{j}=13500kgm/s$