a 43.7 kg student runs down the sidewalk and jumps with a horizontal speed of 4.48 m/s onto a stationary skateboard. the student and the skateboard move down the sidewalk with a speed of 4.25m/s. find the mass of the skateboard in units of kg. how fast would the student have to jump to have a final speed of 6.94 m/s?
Uhm this is not a direct answer but there was a question asked about this through out the Website time of 3:00 p.m -5:00 p.m
You may want to check it out so you can have atleast an equation to do this.
To find the mass of the skateboard, we can use the principle of conservation of momentum. According to the principle, the total momentum before the jump is equal to the total momentum after the jump.
Before the jump:
Momentum of the student = mass of the student × speed of the student
Momentum of the student = (43.7 kg) × (4.48 m/s)
After the jump:
Momentum of the student and skateboard = (mass of the student + mass of the skateboard) × (final speed)
Since the student and skateboard move together at 4.25 m/s after the jump, the final speed is 4.25 m/s.
Using the principle of conservation of momentum, we can set the two momenta equal to each other and solve for the mass of the skateboard:
(43.7 kg) × (4.48 m/s) = (mass of the student + mass of the skateboard) × (4.25 m/s)
Now, let's solve for the mass of the skateboard:
(43.7 kg) × (4.48 m/s) = (mass of the student + mass of the skateboard) × (4.25 m/s)
(43.7 kg × 4.48 m/s) - (43.7 kg × 4.25 m/s) = mass of the skateboard × (4.25 m/s)
194.936 kg·m/s - 185.925 kg·m/s = mass of the skateboard × (4.25 m/s)
9.011 kg·m/s = mass of the skateboard × (4.25 m/s)
mass of the skateboard = 9.011 kg·m/s / (4.25 m/s)
Therefore, the mass of the skateboard is approximately 2.118 kg.
To determine how fast the student would have to jump to have a final speed of 6.94 m/s, we can set up a new equation using the principle of conservation of momentum.
Before the jump:
Momentum of the student = mass of the student × speed of the student
Momentum of the student = (43.7 kg) × (velocity to be determined)
After the jump:
Momentum of the student and skateboard = (mass of the student + mass of the skateboard) × (final speed)
Setting the two momenta equal to each other:
(43.7 kg) × (velocity to be determined) = (mass of the student + 2.118 kg) × (6.94 m/s)
Now, solve for velocity to be determined:
(43.7 kg) × (velocity to be determined) = (43.7 kg + 2.118 kg) × (6.94 m/s)
velocity to be determined = [(43.7 kg + 2.118 kg) × (6.94 m/s)] / (43.7 kg)
After calculating the expression, the velocity to be determined is approximately 7.04 m/s.