A 41.2 kg student runs down the sidewalk and
jumps with a horizontal speed of 4.36 m/s onto a stationary skateboard. The student and skateboard move down the sidewalk with a speed of 4.12 m/s.
a. Find the mass of the skateboard (in kg)
b. How fast would the student have to jump to have a final speed of 5.76 m/s? (in m/s)
a. To find the mass of the skateboard, we can use the principle of conservation of momentum. The initial momentum of the student before jumping onto the skateboard should be equal to the final momentum of both the student and the skateboard after jumping.
We can calculate the initial momentum using the equation:
momentum = mass * velocity
The initial momentum of the student is given by:
momentum_student_initial = mass_student * velocity_student_initial
The final momentum of the student and the skateboard is given by:
momentum_final = (mass_student + mass_skateboard) * velocity_final
Since the student jumps with a horizontal speed of 4.36 m/s and the combined velocity of the student and the skateboard is 4.12 m/s, we have:
momentum_student_initial = momentum_final
mass_student * velocity_student_initial = (mass_student + mass_skateboard) * velocity_final
Plugging in the given values:
41.2 kg * 4.36 m/s = (41.2 kg + mass_skateboard) * 4.12 m/s
Solving this equation for mass_skateboard will give us the mass of the skateboard.
b. To determine how fast the student would have to jump to have a final speed of 5.76 m/s, we can again use the principle of conservation of momentum.
Using the same equation as before:
momentum_student_initial = momentum_final
mass_student * velocity_student_initial = (mass_student + mass_skateboard) * velocity_final
This time, plugging in the given final speed of 5.76 m/s and solving the equation for velocity_student_initial will give us the required initial speed of the jump.