Answer :
Explanation:
Momentum is conserved.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Initially, both the astronaut and the tool are at rest, so u₁ = u₂ = 0 m/s.
After throwing the tool, the tool has a velocity of v₂ = 3.20 m/s.
(68.5 kg) (0 m/s) + (2.25 kg) (0 m/s) = (68.5 kg) v + (2.25 kg) (3.20 m/s)
0 = (68.5 kg) v + 7.2 kg m/s
v = -0.105 m/s
The astronaut moves at a speed of 0.105 m/s in the opposite direction.
The speed and the direction of the astronaut is 0.105 m/s in opposite direction to the motion of the tool.
Note: The momentum of the astronaut is equal and opposite to the momentum of the tool
To calculate the speed and the direction of the astronaut, we use the formula below.
Formula:
- MV = -mv.............. Equation 1
Where:
- M = mass of the astronaut
- V = speed of the astronaut
- m = mass of the tool
- v = speed of the tool.
make V the subject of the equation
- V = mv/M................. Equation 2
From the question,
Given:
- m = 2.25 kg
- M = 68.5 kg
- v = 3.2 m/s
Substitute these values into equation 2
- V = (2.25×3.2)/68.5
- V = 0.105 m/s in opposite direction to the speed of the tool.
Hence, The speed and the direction of the astronaut is 0.105 m/s in opposite direction to the motion of the tool.
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