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

Answer:

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

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

$20\times4.5=65v_{x}$

$v_{x}=1.385m/s$

Momentum in the y- direction

in the y direction, $v_{1}= 0$. this makes $m_{1}v_{1}=0$

hence we have

$45\times2.0=65v_{y}$

$v_{y}=1.385m/s$

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

$Tan^{-1}(\frac{1.385}{1.385})=45degrees$

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