Question

A 20 g ball of clay traveling east at 4.5 m/s collides with a 45 g ball of clay traveling north at 2.0 m/s. You may want to review (Page 280) . Part A What is the speed of the resulting 65 g ball of clay

Answer 1

The ball travels with a speed of 1.96 m/s in a North East direction

Step-by-step explanation:

Based on the law of conservation of linear momentum, we have that

`m_(1)v_(1)+m_(2)v_(2)=(m_(1)+m_(2))v`

Since this problem involves motion in both the x and y coordinates, we will solve it in the separate coordinates, and then find the resultant as our answer.

Momentum in the x- direction

in the x direction,
`v_(2)= 0`. this makes
`m_(2)v_(2)=0`

hence we have

`20*4.5=65v_(x)`

`v_(x)=1.385m/s`

Momentum in the y- direction

in the y direction,
`v_(1)= 0`. this makes
`m_(1)v_(1)=0`

hence we have

`45*2.0=65v_(y)`

`v_(y)=1.385m/s`

The resultant of the two vectors can be found using Pythagoras' theorem

`v=\sqrt{1.385^(2)+1.385^(2)} =1.959`

The direction of the resultant vector is found as

`Tan^(-1)((1.385)/(1.385))=45degrees`

Hence the ball moves with a velocity of 1.96m/s in a North East direction