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
[tex]m_{1}v_{1}+m_{2}v_{2}=(m_{1}+m_{2})v[/tex]
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, [tex]v_{2}= 0[/tex]. this makes [tex]m_{2}v_{2}=0[/tex]
hence we have
[tex]20\times4.5=65v_{x}[/tex]
[tex]v_{x}=1.385m/s[/tex]
Momentum in the y- direction
in the y direction, [tex]v_{1}= 0[/tex]. this makes [tex]m_{1}v_{1}=0[/tex]
hence we have
[tex]45\times2.0=65v_{y}[/tex]
[tex]v_{y}=1.385m/s[/tex]
The resultant of the two vectors can be found using Pythagoras' theorem
[tex]v=\sqrt{1.385^{2}+1.385^{2}} =1.959[/tex]
The direction of the resultant vector is found as
[tex]Tan^{-1}(\frac{1.385}{1.385})=45degrees[/tex]
Hence the ball moves with a velocity of 1.96m/s in a North East direction
