Question

Assume forward is positive. The September 14, 1987, issue of the New York Times had a mass of 5.6 kg. Suppose a skateboarder picks up a copy of this issue to have a look at the comic pages while rolling backward on the skateboard. Upon realizing that the New York Times doesn’t have a “funnies” section, the skateboarder promptly throws the entire issue in a recycling container. The newspaper is thrown forward with a speed of 7.5 m/s. When the skater throws the newspaper away, he rolls backward at a speed of 1.4 m/s. If the combined mass of the skateboarder and skateboard is assumed to be 50.3 kg, what is the initial velocity of the skateboarder and newspaper before the newspaper is recycled? Round to the hundredths.

Answer 1

The initial momentum of the system can be expressed as,

`p_i=(m_1+m_2)u`

The final momentum of the system can be given as,

`p_f=m_1v_1+m_2v_2`

According to conservation of momentum,

`p_i=p_f`

Plug in the known expressions,

`\begin{gathered} (m_1+m_2)u=m_1v_1+m_2v_2 \\ u=\frac{m_1v_1+m_2v_2}{m_1+m_2_{}} \end{gathered}`

Since the newspaper moves in the backward direction, therefore it is tekan as negative. Substitute the known values,

`\begin{gathered} u=\frac{(5.6\text{ kg)(7.5 m/s)+(50.3 kg)(-1.4 m/s)}}{(5.6\text{ kg+50.3 kg)}} \\ =\frac{42\text{ kgm/s-}70.42\text{ kgm/s}}{55.9\text{ kg}} \\ =-\frac{28.42\text{ kgm/s}}{55.9\text{ kg}} \\ =-0.508\text{ m/s} \end{gathered}`

Thus, the initial velocity of skateboarder and newspaper is -0.508 m/s where negative sign indicates the backward direction of motion.