A space shuttle has a mass of 110 kg with her space suit on. She is on a spacewalk and takes up a full can of spray with a mass of 20 kg. Relative to the space shuttle, she is at rest. She then holds the can directly in front of the centre of Mass to avoid rotation and releases 5.5 kg of spray at a speed of 15.6 m/s. Her speed, relative to the Space Shuttle, when she has stopped the spray is approximately a.bc m\s.
her momentum back = spray momentum forward
(110+20-5.5) v = 5.5 * 15.6
Well, let's break it down, space ranger! We have a space shuttle with a mass of 110 kg and a spacewalking astronaut with her space suit on. Then she grabs a can of spray with a mass of 20 kg. When she sprays out 5.5 kg of the spray at a speed of 15.6 m/s, she needs to conserve momentum.
Now, the total momentum before she sprays is given by the equation:
(mass of the astronaut + mass of the shuttle) × 0 m/s = (mass of the astronaut + mass of the shuttle + mass of the expelled spray) × speed of the astronaut
Plugging in the values we have:
(110 kg + 20 kg) × 0 m/s = (110 kg + 20 kg + 5.5 kg) × speed of the astronaut
Now, solving for the speed of the astronaut:
130 kg × 0 m/s = 135.5 kg × speed of the astronaut
Since anything multiplied by zero is zero, we can just ignore the left side of the equation:
0 = 135.5 kg × speed of the astronaut
Therefore, speed of the astronaut = 0 m/s!
Since the astronaut is at rest relative to the space shuttle after spraying the can, her speed relative to the space shuttle is approximately 0 m/s. So, a.bc = 0!
Let's keep the momentum of jokes going, space cowboy! Is there anything else I can blast off and answer for you?
To solve for the speed of the astronaut relative to the space shuttle when she has stopped the spray, we can use the principle of conservation of momentum.
1. Find the initial momentum of the astronaut and the can of spray:
Momentum = mass × velocity
Initial momentum of astronaut and can = (mass of astronaut + mass of can) × velocity of astronaut relative to the shuttle
Initial momentum = (110 kg + 20 kg) × 0 m/s (since the astronaut is at rest relative to the shuttle)
Initial momentum = 0 kg⋅m/s
2. Find the final momentum of the astronaut and the can after releasing the spray.
Final momentum = (mass of astronaut + mass of can + mass of released spray) × velocity of astronaut relative to the shuttle
Final momentum = (110 kg + 20 kg + 5.5 kg) × v (let v be the velocity of the astronaut relative to the shuttle)
Final momentum = (135.5 kg) × v
3. Apply the conservation of momentum principle:
Initial momentum = Final momentum
0 kg⋅m/s = (135.5 kg) × v
4. Solve for v:
v = 0 m/s / 135.5 kg
v ≈ 0 m/s
Therefore, the speed of the astronaut relative to the space shuttle when she has stopped the spray is approximately 0 m/s.
To determine the speed of the astronaut after she has stopped spraying, we can apply the principle of conservation of momentum. The total momentum before she sprays is equal to the total momentum after she sprays.
Before spraying:
The astronaut's mass, including her space suit, is 110 kg.
The can of spray has a mass of 20 kg.
Total initial mass (m1) = 110 kg + 20 kg = 130 kg
After spraying:
The astronaut's mass is still 110 kg.
The mass of the remaining spray is 20 kg - 5.5 kg = 14.5 kg.
Total final mass (m2) = 110 kg + 14.5 kg = 124.5 kg
Let v1 be the initial velocity of the astronaut (which is zero since she is at rest relative to the space shuttle) and v2 be her final velocity after stopping the spray. We want to find v2.
Using the conservation of momentum:
m1 * v1 = m2 * v2
Plugging in the values:
130 kg * 0 m/s = 124.5 kg * v2
Simplifying,
0 = 124.5 kg * v2
Dividing both sides by 124.5 kg,
0 / 124.5 kg = v2
Therefore, the final velocity of the astronaut, relative to the space shuttle, after she has stopped spraying is 0 m/s.