an astronaut floating in space is separated from his ship. his mass in 85.0kg and he is 10.0m from ship. he throws a wrench moss is .8000kg opposite direction with a velocity of 20m/s. how long will it take him to reach the ship?
To find out how long it will take for the astronaut to reach the ship, we can use the principle of conservation of momentum.
1. First, we need to calculate the initial momentum of the astronaut and the wrench. Momentum is calculated as the product of mass and velocity: momentum = mass × velocity.
The initial momentum of the astronaut is given by: momentum_astronaut = (mass_astronaut × velocity_astronaut)
= (85.0 kg × 0 m/s) = 0 N·s
The initial momentum of the wrench is: momentum_wrench = (mass_wrench × velocity_wrench)
= (0.8000 kg × 20 m/s) = 16 N·s
2. Since momentum is conserved, the total momentum of the system (astronaut + wrench) before the throw is equal to the total momentum after the throw.
Total momentum before = Total momentum after
Therefore:
0 N·s + 16 N·s = (total mass × final velocity)
3. To find the final velocity, we need to consider the fact that when the astronaut throws the wrench, it pushes him in the opposite direction. So the final velocity of the astronaut and the wrench together is equal to their initial velocity minus the velocity of the wrench being thrown. Since the astronaut and the wrench have opposite directions, we'll use a negative sign for the wrench's velocity.
Final velocity = initial velocity - velocity of the wrench
The initial velocity of the astronaut is 0 m/s, and the velocity of the wrench being thrown is 20 m/s in the opposite direction. Therefore:
Final velocity = 0 m/s - (-20 m/s) = 20 m/s
4. Now, we can rearrange the equation from step 2 to solve for the total mass:
Total mass = (total momentum after) / final velocity = (16 N·s) / (20 m/s) = 0.8 kg
5. To find the time it takes for the astronaut to reach the ship, we can use the equation for average velocity: velocity = displacement / time. Rearranging the formula, we get:
time = displacement / velocity
Since the astronaut is 10.0 m away from the ship and their final velocity is 20 m/s, we can substitute in these values to get:
time = (displacement) / (velocity) = (10.0 m) / (20 m/s) = 0.5 seconds
Therefore, it will take the astronaut 0.5 seconds to reach the ship.