A 56 kg astronaut throws a 5kg wrench at a speed of 3m/s to the right. What is the speed the astronaut will move? Show step by step
Answer (1)
Step-by-Step Solution:Calculate the total initial momentum of the system:Since both the astronaut and the wrench are initially at rest, their initial speeds are 0 m/s.P initial =(m A ×v A,i )+(m W ×v W,i )P initial =(56 kg×0 m/s)+(5 kg×0 m/s)P initial =0 kg⋅m/sCalculate the total final momentum of the system:After the wrench is thrown, both the astronaut and the wrench will have a final momentum.P final =(m A ×v A,f )+(m W ×v W,f )We know m A , m W , and v W,f . We need to find v A,f .Apply the Law of Conservation of Momentum:According to the law, the total initial momentum must equal the total final momentum:P initial =P final 0=(m A ×v A,f )+(m W ×v W,f )Substitute the known values and solve for v A,f :0=(56 kg×v A,f )+(5 kg×3 m/s)0=56⋅v A,f +15 kg⋅m/sNow, isolate v A,f :−15 kg⋅m/s=56 kg⋅v A,f v A,f = 56 kg−15 kg⋅m/s v A,f ≈−0.267857 m/sInterpret the result:The negative sign indicates that the astronaut will move in the opposite direction to the wrench. Since the wrench was thrown to the right, the astronaut will move to the left.
