A stationary skateboarder I with a mass of 50 kg pushes a stationary skateboarder II with a mass of 75 kg. After the push the skateboarder II moves with a velocity of 2 m/s to the right. What is the velocity of the skateboarder I?
To find the velocity of skateboarder I, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before and after the push should remain the same.
Momentum (p) is given by the formula:
p = mass × velocity
Let's denote the initial velocity of skateboarder I as v₁, and the final velocity of skateboarder I as v₂. The initial velocity of skateboarder II is zero.
Initially, the total momentum is:
p_initial = (mass₁ × velocity₁) + (mass₂ × velocity₂)
= (50 kg × v₁) + (0 kg × 0 m/s) (since skateboarder II is stationary)
After the push, skateboarder II moves with a velocity of 2 m/s to the right, so we can write:
p_final = (mass₁ × velocity₁) + (mass₂ × velocity₂)
= (50 kg × v₂) + (75 kg × 2 m/s)
Since the total momentum is conserved, we can equate the initial and final momenta:
p_initial = p_final
(50 kg × v₁) = (50 kg × v₂) + (75 kg × 2 m/s)
Now let's solve this equation for v₁ to find the velocity of skateboarder I.
(50 kg × v₁) = (50 kg × v₂) + (75 kg × 2 m/s)
50 kg × v₁ = 50 kg × v₂ + 150 kg × 1 m/s (simplifying)
Dividing both sides by 50 kg, we get:
v₁ = v₂ + 3 m/s
Therefore, the velocity of skateboarder I is equal to the velocity of skateboarder II plus 3 m/s in the same direction.
To solve this problem, we can use the principle of conservation of momentum. The total momentum before the push is equal to the total momentum after the push.
The momentum of an object is calculated by multiplying its mass by its velocity. In this case, the momentum of skateboarder I before the push is zero because they are stationary (mass of 50 kg), and the momentum of skateboarder II is also zero before the push because they are stationary (mass of 75 kg).
Total momentum before the push = momentum of I before the push + momentum of II before the push = 0 + 0 = 0 kg·m/s
After the push, the skateboarder II moves with a velocity of 2 m/s to the right. Let's assume the velocity of skateboarder I after the push is V.
Total momentum after the push = momentum of I after the push + momentum of II after the push = mass of I * V + mass of II * 2 m/s
Using the principle of conservation of momentum, we can set the total momentum before the push equal to the total momentum after the push:
0 kg·m/s = 50 kg * V + 75 kg * 2 m/s
0 = 50V + 150
50V = -150
V = -3 m/s
Therefore, the velocity of skateboarder I after the push is -3 m/s to the left.
6. A stationary skateboarder I with a mass of 50 kg pushes a stationary skateboarder II with a mass of 75 kg. After the push the skateboarder II moves with a velocity of 2 m/s to the right. What is the velocity of the skateboarder I? *
momentum is conserved
(75 * 2) + (50 * v) = 0