Respuesta :
Answer:
a) 3.632 m/s
b) 0.462 m/s
Explanation:
Using the law of conservation of momentum:
[tex]m_{1} u_{1} + m_{2} u_{2}= m_{1} V_{1} + m_{2} V_{2}[/tex]..........(1)
[tex]m_{1} = 0.30 kg\\u_{1} = 2.4 m/s\\m_{2} = 0.80 kg\\u_{2} = 0 m/s[/tex]
Substituting the above values into equation (1) and make V2 the subject of the formula:
[tex]0.3(2.4) + 0.80(0)= 0.3 V_{1} + 0.8 V_{2}\\[/tex]
[tex]V_{2} = \frac{0.72 - 0.3 V_{1}}{0.8}[/tex]..................(2)
Using the law of conservation of kinetic energy:
[tex]0.5m_{1} u_{1} ^{2} + 1.2 = 0.5m_{1} V_{1} ^{2} + 0.5m_{2} V_{2} ^{2}\\0.5(0.3) (2.4) ^{2} + 1.2 = 0.5(0.3) V_{1} ^{2} + 0.5(0.8)V_{2} ^{2}\\[/tex]
[tex]2.064 = 0.15 V_{1} ^{2} + 0.4V_{2} ^{2}[/tex].......(3)
Substitute equation (2) into equation (3)
[tex]2.064 = 0.15 V_{1} ^{2} + 0.4(\frac{0.72 - 0.3V_{1} }{0.8}) ^{2}\\2.064 = 0.15 V_{1} ^{2} + 0.4(\frac{0.5184 - 0.432V_{1} + 0.09V_{1} ^{2} }{0.64}) \\1.32096 = 0.096 V_{1} ^{2} + 0.20736 - 0.1728V_{1} + 0.036V_{1} ^{2} \\0.132 V_{1} ^{2} - 0.1728V_{1} - 1.1136 = 0\\V_{1} = 3.632 m/s[/tex]
Substituting [tex]V_{1}[/tex] into equation(2)
[tex]V_{2} = \frac{0.72 - 0.3 *3.632}{0.8}\\V_{2} = \frac{0.72 - 0.3 *(3.632)}{0.8}\\V_{2} = 0.462 m/s[/tex]
