A student standing on a stationary skateboard tosses a textbook with a mass of mb = 1.95 kg to a friend standing in front of him. The student and the skateboard have a combined mass of mc = 86 kg and the book leaves his hand at a velocity of vb = 4.54 m/s at an angle of 38° with respect to the horizontal.

The question is not complete. The missing part of the question says;

a)Calculate the magnitude of the velocity of the student, v_s in meters per second.

b)What is the magnitude of the momentum, pe, which was transferred from the skateboard to the the Earth during the time the book is being thrown (in kilogram meters per second)?

A) v_s = 0.081 m/s in an opposite direction to that of the book.

B) P_e = 5.45 Kg.m/s in downward direction.

Explanation:

We are given;

Mass of the book m_b = 1.95 kg

Mass of the student and the skateboard m_c = 86 kg

Velocity of the book v_b = 4.54 m/s

Angle of projection θ = 38°

A) Using principle of conservation of momentum;

The horizontal component of the velocity of book is given as;

V_bx = V_b cos θ

Now, the book and the student are initially at rest, and so their initial momentum is zero in both horizontal and vertical direction.

Thus,

Initial momentum = final momentum

0 = m_b•v_b•cos θ + m_c•v_s

Let's make v_s the subject of the formula;

v_s = -[m_b•v_b•cos θ]/m_c

Plugging in the relevant values to get ;

v_s = -[1.95•4.54•cos 38]/86

v_s = -0.081 m/s

The minus sign indicates that the direction of the velocity of the student is opposite to that of the book.

B) The vertical component of the velocity of book is given as;

V_by = V_b sin θ

In this vertical direction, the student is not moving, because he transfers his momentum. The momentum transferred to the earth is equal to the vertical component of the book’s momentum in magnitude but opposite in direction. Thus;

P_e = -P_ey

P_e = - m_b•v_b•sinθ

Thus, plugging in the relevant values to get ;

P_e = -1.95 x 4.54 sin38

P_e = -5.45 Kg.m/s

The minus sign indicates that the direction of momentum is downwards

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