Question

The momentum of a system before a collision is 2.4 × 103 kilogram meters/second in the x-direction and 3.5 × 103 kilogram meters/second in the y-direction. What is the magnitude of the resultant momentum after the collision if the collision is inelastic?

A. 1.7 × 103 kilogram meters/second
B. 2.1 × 103 kilogram meters/second
C. 3.4 × 103 kilogram meters/second
D. 4.2 × 103 kilogram meters/second
E. 5.7 × 103 kilogram meters/second ...?

Answer 1

Option D -
`4.2* 10^3` kilogram meters/second.

Explanation:

Given : The momentum of a system before a collision is
`2.4 * 10^3` kilogram meters/second in the x-direction and
`3.5 * 10^3` kilogram meters/second in the y-direction.

To find : What is the magnitude of the resultant momentum after the collision if the collision is inelastic?

Solution :

In inelastic,

The magnitude of the resultant momentum after the collision (and before) can be determined by using the Pythagorean theorem.

`c^2 = a^2 + b^2`

Where, a is the momentum before collision
`a=2.4 * 10^3`

b is the momentum after collision
`b=3.5 * 10^3`

c is the total amount of momentum before and after collision.

Substitute the value,

`c^2 = (2.4*10^3)^2 + (3.5*10^3)^2`

`c^2 =5760000+ 12250000`

`c=√(18010000)`

`c=4243.819`

`c=4.2* 10^3` kg m/s

Therefore, Option D is correct.

The magnitude of the resultant momentum after the collision if the collision is inelastic is
`4.2* 10^3` kilogram meters/second.

Answer 2

If inelastic, then the total amount of system momentum before the collision (and after) can be determined by using the Pythagorean theorem. It is expressed as:

c^2 = a^2 + b^2
c^2 = (2.4x10^3)^2 + (3.5x10^3)^2
c = 4.2 x10^3 kilogram meters/second -------> OPTION C