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Aliya is rolling along on her 4.0-kg long board with a constant speed of 3.0 m/s when she jumps off the back and continues forward with a velocity of 2.0 m/s relative to the ground. This causes the long board to go flying forward with aspeed of 15.5 m/s relative to the ground. What is Aliya’s mass?

Answer :

Given data

*The given mass of the longboard is M = 4.0 kg

*Alia is rolling along on her longboard at a speed is v = 3.0 m/s

*Alia is moving at a speed is v_1 = 2.0 m/s

*Speed of the longboard relative to the ground is v_2 = 15.5 m/s

The Alia's mass is calculated by the conservation of momentum as

[tex]\begin{gathered} P_i=P_f \\ mv_1+Mv_2=(m+M)v \end{gathered}[/tex]

*Here m is the Alia's mass

Substitute the known values in the above expression as

[tex]\begin{gathered} m(2.0)+(4.0)(15.5)=(m+4.0)(3.0) \\ 2m+62.0=3m+12.0 \\ m=50.0\text{ kg} \end{gathered}[/tex]

Hence, Alia's mass is m = 50.0 kg

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