ANSWER
[tex]46.24\operatorname{kg}[/tex]EXPLANATION
Parameters given:
Mass of student, m = 64.0 kg
Initial velocity of student, u = 4.53 m/s
Initial velocity of skateboard, U = 0 m/s
Final velocity of student and skateboard, v = 2.63 m/s
To solve this problem, we have to apply the law of conservation of momentum which states that the total momentum of a system is constant.
This implies that:
[tex]mu+MU=mv+MV[/tex]The final velocity of the student and skateboard are equal. This implies that:
[tex]mu+MU=(m+M)v[/tex]where M = mass of skateboard
Substitute the given values into the equation and solve for M:
[tex]\begin{gathered} (64\cdot4.53)+(M\cdot0)=(64+M)\cdot2.63 \\ 289.92+0=(64+M)\cdot2.63 \\ \Rightarrow64+M=\frac{289.92}{2.63} \\ 64+M=110.24 \\ \Rightarrow M=110.24-64 \\ M=46.24\operatorname{kg} \end{gathered}[/tex]That is the mass of the skateboard.
