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An astronaut with a mass of #85 kg# is floating in space. If the astronaut throws a #5 kg# object at a speed of #2/3 m/s#, how much will his speed change by?

Answer 1

William Audy

Since he was initially at rest, his speed change and final speed are the same: -0.039 m/s.

Momentum in the system is preserved.

#"Momentum before = momentum after"#

#(m_1+m_2)*u = m_1*v_1 + m_2*v_2#

#(85 "kg" + 5 "kg")*0 = 85 "kg"*v_1 + 5 "kg"*2/3 m/s#

#85 "kg"*v_1 = -5 "kg"*2/3 m/s#

#v_1 = (-5 cancel("kg")*2/3 m/s)/(85 cancel("kg")) = -0.039 m/s#

Note: If he had been moving initially, the original mass of 90 kg would have been a factor. However, in this case, forgetting that he initially carried that 5 kg object with him is not an issue because the original velocity was zero.

Hope this is helpful, Steve.

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Answer 2

Adrian Ayala

To find the change in velocity, we can use the principle of conservation of momentum. The initial momentum of the system (astronaut + object) is equal to the final momentum of the system.

Initial momentum = final momentum
(85 kg) * (initial velocity of astronaut) = (85 kg + 5 kg) * (final velocity of astronaut)

Initial momentum = 85 kg * initial velocity of astronaut
Final momentum = (85 kg + 5 kg) * final velocity of astronaut

(85 kg) * (initial velocity of astronaut) = (90 kg) * (final velocity of astronaut)

Solve for the final velocity of the astronaut:

85 kg * initial velocity of astronaut = 90 kg * final velocity of astronaut
final velocity of astronaut = (85 kg * initial velocity of astronaut) / 90 kg
final velocity of astronaut = (85/90) * initial velocity of astronaut

Substitute the values:

final velocity of astronaut = (85/90) * (2/3) m/s
final velocity of astronaut = 1/2 m/s

Change in velocity = final velocity - initial velocity
Change in velocity = (1/2 m/s) - (0 m/s)
Change in velocity = 1/2 m/s

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.