Answer:
a) The mass of the skateboard is 18.4 kg.
b) The student would have to jump with a velocity of 7.85 m/s to have a final speed of 6.05 m/s.
Step-by-step explanation:
a) The problem states that a 47 kg student runs down the sidewalk and jumps with a horizontal speed of 4.33 m/s onto a stationary skateboard. After the student jumps onto the skateboard, the student and skateboard move down the sidewalk with a speed of 4.08 m/s. We need to find the mass of the skateboard.
To solve this problem, we can use the principle of conservation of momentum, which says that the total momentum of a system remains constant when there are no external forces acting on it. We can write the equation as:
(m_student * v_student) + (m_skateboard * 0) = (m_student + m_skateboard) * v_final
where m_student is the mass of the student, v_student is the velocity of the student before jumping onto the skateboard, m_skateboard is the mass of the skateboard, and v_final is the final velocity of the student and skateboard after the jump.
Since the skateboard is initially at rest, its velocity is zero. We can simplify the equation as:
(m_student * v_student) = (m_student + m_skateboard) * v_final
Substituting the given values, we get:
(47 kg * 4.33 m/s) = (47 kg + m_skateboard) * 4.08 m/s
Solving for m_skateboard, we get:
m_skateboard = 18.4 kg
Therefore, the mass of the skateboard is 18.4 kg.
b) The problem asks how fast the student would have to jump to have a final speed of 6.05 m/s.
To solve this problem, we can again use the principle of conservation of momentum. The equation would be the same as before:
(m_student * v_student) + (m_skateboard * 0) = (m_student + m_skateboard) * v_final
where v_final is the final velocity of the student and skateboard, and we need to find v_student, the velocity of the student before jumping onto the skateboard.
We can rearrange the equation as:
v_student = (m_student + m_skateboard) * v_final / m_student
Substituting the given values, we get:
v_student = (47 kg + 18.4 kg) * 6.05 m/s / 47 kg
Simplifying, we get:
v_student = 7.85 m/s
Therefore, the student would have to jump with a velocity of 7.85 m/s to have a final speed of 6.05 m/s.