An astronaut with a mass of 100 kg throws a wrench with a mass of 2 kg at a velocity of 5 m/s. What is the resulting recoil velocity of the astronaut if both the wrench and astronaut were initially at rest together?
momentum after = momentum before = 0
0 = 2*5 - 100 v
v = 10/100 = 0.1
M1*V1 = -M2*V2.
100*V1 = -2*5,
V1 = -0.1 m/s.
To find the resulting recoil velocity of the astronaut, we can use the principle of conservation of momentum. According to this principle, the total momentum before the throw is equal to the total momentum after the throw.
The momentum of an object is given by the product of its mass and velocity. Therefore, the initial momentum before the throw is:
Initial momentum = (Mass of astronaut + Mass of wrench) * Initial velocity
Since both the astronaut and the wrench were initially at rest together, their initial velocity is 0. Thus, the initial momentum is also 0.
Therefore, the final momentum after the throw is also 0, which means the astronaut must move in the opposite direction to compensate for the momentum of the thrown wrench.
Thus, the resulting recoil velocity of the astronaut is 0 m/s.
To find the resulting recoil velocity of the astronaut, we can use the principle of conservation of momentum. According to this principle, the total momentum before the wrench is thrown should be equal to the total momentum after the wrench is thrown.
The total momentum of an object is given by the product of its mass and velocity. Therefore, we need to calculate the initial momentum of the system (astronaut and wrench) and the final momentum of the system.
Initial momentum of the system:
The astronaut and the wrench are initially at rest together, so the initial momentum of the system is zero.
Final momentum of the system:
The momentum of the wrench after it is thrown can be calculated by multiplying its mass (2 kg) with its velocity (5 m/s). This gives us a final momentum of 10 kg*m/s.
According to the principle of conservation of momentum, the final momentum of the system (10 kg*m/s) should be equal to the negative of the final momentum of the astronaut. Let's denote the resulting recoil velocity of the astronaut as v.
Final momentum of the astronaut:
The mass of the astronaut is given as 100 kg. Using the formula for momentum, we have:
P = m * v,
where P is momentum, m is mass, and v is velocity.
Since the initial momentum is zero and the final momentum is -10 kg*m/s, we have:
-10 kg*m/s = 100 kg * v,
Solving for v, we find:
v = -10 kg*m/s / 100 kg = -0.1 m/s.
Therefore, the resulting recoil velocity of the astronaut would be -0.1 m/s (negative because it is in the opposite direction of the thrown wrench).