Answer:
(a) 4.83 m/s to the left
(b) 1224 J
Explanation:
Using the law of conservation, the initial momentum equals the final momentum. Taking left as positive while right as negative then
momentum, p=mv where m is mass and v is velocity
After the collision, the canoe keep their same masses
[tex]m_1v_1+m_2v_2=m_1v_3+m_2v_4[/tex]
m and v represent mass and velocity respectively, the subscripts 1 and 2 are the initial velocities and masses while subscripts 3 and 4 are final velocities
Substituting [tex]m_1[/tex] for 16 Kg, [tex]m_2[/tex] for 4 Kg, [tex]v_1[/tex] for 12 m/s, [tex]v_2[/tex] for -6 m/s since it's towards right and we already mentioned that right is negative, [tex]v_3[/tex] for 22.7 m/s then
[tex](16 Kg\times 12 m/s)+(4 Kg\times -6 m/s)=(16 Kg\times v_4)+ (4 Kg\times 22.7 m/s)[/tex]
[tex]v_4=\frac {77.2}{16}=4.825 m/s\approx 4.83 m/s[/tex] hence direction is to the left
(b)
We know that kinetic energy is given by [tex]0.5mv^{2}[/tex] and by substituting the given values of mass and velocity, in this case not considering direction then we add the values of the two objects in question, and get the total before, and add the values of the two objects after and get the total after
Kinetic energy before collision=KE=[tex]0.5mv^{2}=0.5(16*12^{2}+4*6^{2})=1224 J[/tex]
Kinetic energy after collision=KE=
[tex]0.5mv^{2}=0.5(16 Kg\times 4.83^{2}+ 4 Kg\times 22.7^{2})=1217.211 J[/tex]
The two values of KE before and after collision are almost equal hence we conclude that energy is conserved.
