Two ice skaters stand face to face and "push off" and travel directly away from each other. The boy has a velocity of 5 m/s and he weighs 750 N. The girl weighs 480 N. What is the girl's velocity?
conserve momentum:
750*5 = 480v
Now just find v
Yeah, yeah, the formula is p=mv, but the same factor of g is on both sides of the equation, so it cancels out.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the push off is equal to the total momentum after the push off.
The momentum of an object is defined as the product of its mass and its velocity. In this case, the momentum before the push off is zero because the two skaters are initially at rest.
Let's denote the girl's velocity as v (unknown) and the boy's velocity as 5 m/s. The boy's mass is related to his weight using the formula weight = mass * gravity, where gravity is approximately 9.8 m/s^2.
The boy's mass (m_boy) can be calculated using the formula weight_boy = m_boy * gravity:
750 N = m_boy * 9.8 m/s^2
m_boy = 750 N / 9.8 m/s^2 ≈ 76.5 kg
Similarly, the girl's mass (m_girl) can be calculated using the formula weight_girl = m_girl * gravity:
480 N = m_girl * 9.8 m/s^2
m_girl = 480 N / 9.8 m/s^2 ≈ 49.0 kg
Since the total momentum before the push off is zero, the total momentum after the push off should also be zero because there are no external forces acting on the system.
The momentum after the push off is given by:
momentum_boy + momentum_girl = m_boy * 5 m/s + m_girl * v
0 = 76.5 kg * 5 m/s + 49.0 kg * v
Simplifying the equation:
0 = 382.5 kg m/s + 49.0 kg * v
To find v, we can rearrange the equation:
49.0 kg * v = -382.5 kg m/s
v = -382.5 kg m/s / 49.0 kg
Calculating the value:
v ≈ -7.81 m/s
Therefore, the girl's velocity is approximately -7.81 m/s, indicating that she is moving in the opposite direction to the boy.
To find the girl's velocity, we can use the principle of conservation of momentum. According to this principle, the total momentum before the push off is equal to the total momentum after the push off.
Momentum is calculated by multiplying the mass of an object by its velocity. Since the mass of the boy is not given, we can use the formula:
momentum = mass * velocity
Before the push off, the boy's momentum is calculated as:
Boy's momentum = boy's mass * boy's velocity
After the push off, the momentum of both the boy and the girl combined is:
Boy's momentum + Girl's momentum = (boy's mass * boy's velocity) + (girl's mass * girl's velocity)
Since they move in opposite directions, the magnitudes of their velocities will be the same, but opposite in sign.
Now let's calculate their momenta. Since the boy's mass is not given, we will use the formula for weight to find it. Weight is calculated by multiplying mass by the acceleration due to gravity (9.8 m/s²):
Boy's mass = Boy's weight / acceleration due to gravity
= 750 N / 9.8 m/s²
Once we have the boy's mass, we can calculate the girl's velocity.
Let's plug the values into the equations:
To find boy's mass:
Boy's mass = 750 N / 9.8 m/s²
Now that we have the boy's mass, we can find the girl's velocity. We know that momentum is conserved, so:
Boy's momentum + Girl's momentum = 0
Therefore,
(boy's mass * boy's velocity) + (girl's mass * girl's velocity) = 0
Substituting in the given values, we have:
[(boy's mass) * 5 m/s] + (480 N * girl's velocity) = 0
Now we can solve for the girl's velocity.