The new speed of 22 kg block is 1.57 m/s
Explanation:
Given-
Mass, [tex]m_{1}[/tex]= 22 kg
speed, [tex]v_{1}[/tex] = 5 m/s
[tex]m_{2}[/tex] = 29 kg
[tex]v_{2i[/tex] = 4.6 m/s
New speed of [tex]m_{2}[/tex], [tex]v_{2f}[/tex] = 7.2 m/s
New speed of [tex]m_{1}[/tex], [tex]v_{1f}[/tex] = ?
This is the case of elastic collision.
So,
[tex]M_{1}[/tex] X [tex]V_{1i}[/tex]+ [tex]M_{2}[/tex] X [tex]V_{2i}[/tex] = [tex]M_{1}[/tex] X [tex]V_{1f}[/tex] + [tex]M_{2}[/tex] X [tex]V_{2f}[/tex]
22 X 5 + 29 X 4.6 = 22 X[tex]V_{1f}[/tex] + 29 X 7.2
22 [tex]V_{1f}[/tex] + 208.8 = 243.4
22 [tex]V_{1f}[/tex]= 34.6
[tex]V_{1f}[/tex]= 1.57 m/s
Therefore, the new speed of 22 kg block is 1.57 m/s