A(n) 61.4 kg astronaut becomes separated from the shuttle, while on a space walk. She finds herself 55.7 m away from the shuttle and moving with zero speed relative to the shuttle. She has a(n) 0.841 kg camera in her hand and decides to get back to the shuttle by throwing the camera at a speed of 12 m/s in the direction away from the shuttle.
How long will it take for her to reach the shuttle? Answer in minutes.
To solve this problem, we can use the principle of conservation of momentum. The total momentum before throwing the camera is zero since the astronaut and the camera have zero total velocity relative to the shuttle.
To find the velocity of the astronaut after throwing the camera, we can use the fact that momentum is conserved:
(mass of astronaut)(velocity of astronaut) + (mass of camera)(velocity of camera) = 0
Using the given values:
(61.4 kg)(velocity of astronaut) + (0.841 kg)(12 m/s) = 0
Solving for the velocity of the astronaut:
(61.4 kg)(velocity of astronaut) = - (0.841 kg)(12 m/s)
velocity of astronaut = - (0.841 kg)(12 m/s) / 61.4 kg
velocity of astronaut ≈ -0.163 m/s
The negative sign indicates that the astronaut is moving away from the shuttle, which makes sense since she threw the camera away from the shuttle.
Next, we can calculate the time it takes for the astronaut to reach the shuttle using the equation:
time = distance / velocity
Using the given values:
time = 55.7 m / 0.163 m/s
time ≈ 341.1 seconds
To convert the time to minutes:
time in minutes = 341.1 seconds / 60 seconds/minute
time in minutes ≈ 5.68 minutes
Therefore, it will take approximately 5.68 minutes for the astronaut to reach the shuttle.