A woman with a mass of 56 kg runs at a speed of 8 m/s and jumps onto a giant 30 kg skateboard initially at rest. What is the combined speed of the woman and the skateboard?
conservation of momentum:
50*8=(50+30)V
solve for V
To find the combined speed of the woman and the skateboard, we can use the principle of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity, so we can calculate the initial momentum of the woman and the final momentum of the woman and the skateboard combined.
The initial momentum of the woman is given by mass times velocity, which is:
Initial momentum of the woman = mass of the woman × velocity of the woman
= 56 kg × 8 m/s
= 448 kg·m/s
Since the skateboard is initially at rest, its initial momentum is zero.
According to the law of conservation of momentum, the total momentum before the jump must be equal to the total momentum after the jump.
So, the final momentum of the woman and the skateboard combined should be equal to the initial momentum of the woman:
Final momentum of the woman and the skateboard = 448 kg·m/s
The total mass after the jump is the sum of the woman's mass and the skateboard's mass:
Total mass after the jump = mass of the woman + mass of the skateboard
= 56 kg + 30 kg
= 86 kg
To find the final speed, we can rearrange the formula for momentum (p = mv) to solve for velocity:
Final speed = Final momentum / Total mass after the jump
Substituting the values we have:
Final speed = 448 kg·m/s / 86 kg
≈ 5.21 m/s
Therefore, the combined speed of the woman and the skateboard after the jump is approximately 5.21 m/s.
To find the combined speed of the woman and the skateboard, we can use the concept of conservation of momentum. The total momentum before the woman jumps onto the skateboard is equal to the total momentum after she lands on it.
The momentum of an object can be calculated by multiplying its mass by its velocity. Therefore, the momentum of the woman before she jumps is given by her mass multiplied by her initial speed:
Momentum of the woman before = mass of the woman × initial speed of the woman
= 56 kg × 8 m/s
= 448 kg·m/s
Since the skateboard is initially at rest, its momentum is zero:
Momentum of the skateboard before = 0 kg × 0 m/s
= 0 kg·m/s
After the woman jumps onto the skateboard, the combined momentum of the woman and the skateboard should be the same as the initial momentum of the woman. Therefore, we have:
Momentum after = Momentum before
(mass of the woman + mass of the skateboard) × combined speed = momentum of the woman before
(56 kg + 30 kg) × combined speed = 448 kg·m/s
86 kg × combined speed = 448 kg·m/s
Dividing both sides by 86 kg, we find:
combined speed = 448 kg·m/s ÷ 86 kg
combined speed ≈ 5.21 m/s
Therefore, the combined speed of the woman and the skateboard is approximately 5.21 m/s.