A 69kg skateboarder, at rest on a frictionless surface, throws a 4.0kg rock with the velocity given by v=3(i hat)+4(jhat), 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?
I have no idea what i am doing please help? Any helpwould be greatly appeciated.
To determine the subsequent velocity of the skateboarder, let's start by considering the principles of conservation of momentum.
Momentum is a vector quantity that depends on both the mass and velocity of an object. In this scenario, we have two objects: the skateboarder and the rock.
The formula for momentum is given by:
Momentum = mass x velocity
For the skateboarder, who is initially at rest, the momentum before the throw is zero. Since momentum is conserved in an isolated system (no external forces acting), the total momentum after the throw should also be zero.
To find the x-component of the subsequent velocity of the skateboarder, we can calculate the initial momentum in the x-direction and equate it to the final momentum in the x-direction.
The initial momentum of the skateboarder in the x-direction is zero because they were at rest.
The final momentum is the sum of the momentum of the skateboarder and the rock. Since the rock is thrown with a given velocity, its momentum can be calculated using the given mass and velocity.
Momentum of the rock = 4.0 kg x (3 i hat + 4 j hat) = 12 i hat + 16 j hat
To calculate the final momentum of the skateboarder in the x-direction, we can set the sum of the x-components of the momenta to zero. This gives us:
0 = 0 + 12 (Equating x-components)
Therefore, the x-component of the subsequent velocity of the skateboarder is zero.
To find the y-component of the subsequent velocity, we follow the same process:
Initial momentum of the skateboarder in the y-direction is zero since they were at rest.
The final momentum is the sum of the momentum of the skateboarder and the rock. Using the given mass and velocity of the rock, we can calculate its momentum in the y-direction.
Momentum of the rock = 4.0 kg x (3 i hat + 4 j hat) = 12 i hat + 16 j hat
To find the final momentum of the skateboarder in the y-direction, we can set the sum of the y-components of the momenta to zero. This gives us:
0 = 0 + 16 (Equating y-components)
Therefore, the y-component of the subsequent velocity of the skateboarder is 16 m/s.
In summary:
X-component of subsequent velocity of skateboarder = 0 m/s
Y-component of subsequent velocity of skateboarder = 16 m/s