Question

A loaded transport truck with a mass of 38000kg is travelling at $1.20m/s$ . What will be the velocity of a 1400kg car if it has the same momentum?
A) $32.57m/s$
B) $30m/s$
C) $15m/s$
D) $32.67m/s$

Answer 1

We can find the momentum of truck (${P_{truck}} = {\text{ }}{m_{truck}} \times {v_{truck}}$). According to the question, the momentum of the truck is equal to the momentum of the car which will help us to find the velocity of the car.

Formula used:
$p = m \times v$
Where, $p$ is the momentum, $m$ is the mass and $v$ is the velocity.

Complete Step by Step Answer:
Let a loaded truck with a mass (${m_{truck}}$) be travelling at the velocity (${v_{truck}}$). Let us assume that the momentum of the truck (${P_{truck}}$) is given as-
${P_{truck}} = {\text{ }}{m_{truck}} \times {v_{truck}}$
From the question, we have -
${m_{truck}} = 38000{\text{ }}kg$
${v_{truck}} = 1.2{\text{ }}km/s$
Now, putting the values in the equation of momentum, we get-

$$\Rightarrow {P_{truck}} = 38000 \times 1.2 \\\ \Rightarrow {P_{truck}} = 45600{\text{ }}kgm/s \\\$$

According to the question, it is given that the momentum of car is equal to momentum of truck i.e.
${P_{truck}} = {P_{car}}$
Let a car with a mass (${m_{car}}$) be travelling at the velocity (${v_{car}}$). Let us assume that the momentum of the car (${P_{car}}$) is given as-
${P_{car}} = {m_{car}} \times {v_{car}}$
or we can write this equation as following,
${v_{car}} = \dfrac{{{P_{car}}}}{{{m_{car}}}}$
From the question, we have
${m_{car}} = 1400kg$
$\Rightarrow {v_{car}} = \dfrac{{45600}}{{1400}}$
$\Rightarrow {v_{car}} = 32.57m/s$

Therefore, the car of mass $1400{\text{ }}kg$ and the same momentum as the truck will have the speed $32.57{\text{ }}m/s$. So, option (A) is correct.

Note:
We know that if a body has a mass $m$ and the velocity $v$ then the momentum of the body is the product of mass of the body and the velocity of the body. The momentum is a vector quantity. momentum is the product of a scalar and a vector. The momentum of the truck and the car are equal. So, we can find the momentum of that vehicle first whose mass and velocity is mentioned.