Answer:
Option D - [tex]4.2\times 10^3[/tex] kilogram meters/second.
Step-by-step explanation:
Given : The momentum of a system before a collision is [tex]2.4 \times 10^3[/tex] kilogram meters/second in the x-direction and [tex]3.5 \times 10^3[/tex] 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.
[tex]c^2 = a^2 + b^2[/tex]
Where, a is the momentum before collision [tex]a=2.4 \times 10^3[/tex]
b is the momentum after collision [tex]b=3.5 \times 10^3[/tex]
c is the total amount of momentum before and after collision.
Substitute the value,
[tex]c^2 = (2.4\times10^3)^2 + (3.5\times10^3)^2[/tex]
[tex]c^2 =5760000+ 12250000[/tex]
[tex]c=\sqrt{18010000}[/tex]
[tex]c=4243.819[/tex]
[tex]c=4.2\times 10^3[/tex] kg m/s
Therefore, Option D is correct.
The magnitude of the resultant momentum after the collision if the collision is inelastic is [tex]4.2\times 10^3[/tex] kilogram meters/second.
