A stationary 100-kg person is initially holding a 50-kg ball while standing on a skateboard. The person throws the ball to the right, and the ball moves (with respect to the ground) with a speed of 12 m/s. The person on the skateboard ____________.
A. moves to the left with a speed of 6 m/s
B. moves to the left with a speed of 4 m/s
C.remains stationary
D.moves to the left with a speed of 12 m/s
100 x = 50*12
x is 6
the ball went right so the person goes left
It is that conservation of momentum thing.
Well, this situation seems like a real "ball-istic" problem! Let's break it down.
When the person throws the ball to the right, according to Newton's third law of motion, there will be an equal and opposite reaction. In other words, the person will experience an equal force in the opposite direction. Since they are initially stationary and are not holding on to anything, they will move to the left to conserve momentum.
But how fast will they move? Well, the mass of the person is 100 kg and the mass of the ball is 50 kg. Let's solve this puzzle!
Using the principle of conservation of momentum, we can say that the momentum of the person and the ball before the throw is equal to the momentum after the throw. The initial momentum of the system is zero because everything is at rest. After the throw, we have:
(100 kg + 50 kg) * V = 50 kg * 12 m/s
Let's do some math magic and solve for V:
(150 kg) * V = 600 kg·m/s
V = 600 kg·m/s ÷ 150 kg
V = 4 m/s
So the person on the skateboard will move to the left with a speed of 4 m/s - Option B! Watch out for that moving skateboard!
To solve this question, we can apply the conservation of momentum principle.
The momentum of an object is given by the product of its mass and velocity.
Initially, the person, ball, and skateboard are all at rest. Therefore, the total initial momentum is zero.
The final momentum is equal to the momentum of the ball after it is thrown.
Given that the ball has a mass of 50 kg and moves to the right with a speed of 12 m/s, we can calculate its momentum:
Momentum of the ball = mass of the ball * velocity of the ball
= 50 kg * 12 m/s
= 600 kg*m/s
Since the total initial momentum was zero, the final momentum of the ball must also be zero.
Now, let's consider the momentum of the person and the skateboard.
Since the final momentum is zero, and the person and the skateboard are connected and have a combined mass of 100 kg, the momentum of the person and the skateboard must also be zero. This means they both move in the opposite direction of the thrown ball.
Therefore, the person on the skateboard moves to the left with a speed of 6 m/s (half the speed of the thrown ball).
The correct answer is:
A. moves to the left with a speed of 6 m/s
To determine the motion of the person on the skateboard, we need to apply the principles of conservation of momentum. The total momentum before the ball is thrown is equal to the total momentum after the ball is thrown.
The momentum of an object is calculated by multiplying its mass by its velocity. Let's represent the person's mass as m1, the ball's mass as m2, the person's velocity as v1, and the ball's velocity as v2.
Before the ball is thrown, the person and the ball are at rest, so their velocities are both zero. This means that the total momentum before throwing the ball is zero.
After the ball is thrown, the person is still on the skateboard, and their velocities are now different. The person's final velocity (v1') can be calculated.
According to the principle of conservation of momentum, the momentum before the ball is thrown is equal to the momentum after the ball is thrown.
m1 * v1 + m2 * v2 = m1 * v1'
Plugging in the given values, where m1 = 100 kg, m2 = 50 kg, and v2 = 12 m/s, we can solve for v1'.
100 kg * 0 m/s + 50 kg * 12 m/s = 100 kg * v1'
0 + 600 kg·m/s = 100 kg * v1'
600 kg·m/s = 100 kg * v1'
Dividing both sides of the equation by 100 kg, we get:
6 m/s = v1'
Therefore, the person on the skateboard moves to the left with a speed of 6 m/s (option A).