A 69kg skateboarder, at rest on a frictionless surface, throws a 4.0kg rock with the velocity given by x=3m/s y=4m/s, where the x and y axes are both in the horizontal plane. What is the x component of the subsequent velocity of the skateboarder? WHat is the y component of th subsequent velocity of the skateboarder?
Do I use the pythagorean theorem?
To solve this problem, you will need to apply the conservation of momentum principle. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is calculated as the product of its mass and velocity:
Momentum = mass * velocity
The x-component of the subsequent velocity of the skateboarder can be found using the conservation of momentum along the x-axis. Since there is no external force acting on the system in the horizontal direction, the total momentum along the x-axis will be conserved.
Initial momentum of the skateboarder = 0 (since they are at rest)
Final momentum of the skateboarder = m_skateboarder * Vx_skateboarder
The momentum of the rock can be calculated as:
Momentum of the rock = m_rock * Vx_rock
Since momentum is conserved, we have:
Initial momentum + Momentum of the rock = Final momentum
0 + m_rock * Vx_rock = m_skateboarder * Vx_skateboarder
Now, let's plug in the given values:
m_rock = 4.0 kg
Vx_rock = 3.0 m/s
m_skateboarder = 69 kg
0 + 4.0 kg * 3.0 m/s = 69 kg * Vx_skateboarder
12 kg*m/s = 69 kg * Vx_skateboarder
Vx_skateboarder = 12 kg*m/s / 69 kg
By dividing, we get Vx_skateboarder = 0.174 m/s (rounded to three decimal places).
Now, let's find the y-component of the subsequent velocity of the skateboarder. Since the motion is occurring in the horizontal plane, and there are no external forces acting in the vertical direction, the y-component of the initial and final velocities would remain the same.
Therefore, the y-component of the subsequent velocity of the skateboarder will be the same as the y-component of the rock's velocity, which is 4 m/s, as given in the question.
So, the x-component of the subsequent velocity of the skateboarder is approximately 0.174 m/s, and the y-component is 4.0 m/s.