Momentum, P,

$\overline{){\mathbf{P}}{\mathbf{=}}{\mathbf{m}}{\mathbf{v}}}$

The horizontal component of velocity,

$\overline{)\begin{array}{rcl}{\mathbf{v}}_{\mathbf{x}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{v}}\mathbf{\right|}\mathbf{}\mathbf{cos}\mathbf{}\mathbf{\theta}\end{array}}$

m_{b} = 1.3 kg, m_{c} = 103 kg, m_{s} = 103 - 1.3 = 101.7kg, v_{b } = 2.98 m/s, θ = 41°

**a)**

Conservation of momentum horizontally:

P_{i} = P_{f}

The momentum of the system initially is 0.

Therefore, the net momentum of the system after the book is thrown is 0.

P_{s} = P_{b}

After throwing the book, the student has the velocity, v_{s}

A student standing on a stationary skateboard tosses a textbook with a mass of m_{b} = 1.3 kg to a friend standing in front of him. The student and the skateboard have a combined mass of m_{c} = 103 kg and the book leaves his hand at a velocity of v_{b } = 2.98 m/s at an angle of 41° with respect to the horizontal.

(a) Write an expression for the magnitude of the velocity of the student, v_{s}, after throwing the book.

(b) Calculate the magnitude of the velocity of the student, v_{s}, in meters per second.

(c) What is the magnitude of the momentum, p_{e}, which was transferred from the skateboard to the Earth during the time the book is being thrown (in kilogram-meters per second)?

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