Construct Your Own an astronaut in deep space cut free from her space ship and needing to get back to it. The astronaut has a few packages that she can throw away to move herself toward the ship. Construct a problem in which you calculate the time it takes her to get back by throwing all the packages at one time compared to throwing them one at a time. Among the things to be considered are the masses involved, the force she can exert on the packages through some distance, and the distance to the ship.
Step-by-step solution Here , we have to calculate the time taken by the astronaut to get back by throwing all the packages at one time compared to throwing them one at a time. So, the solution for the above problem is as follows: Step 1 of 8 An astronaut is at distance 10.0 m from her ship. The exhaust velocity is 3.00 m/s and mass of the Astronaut with the packages is 80 kg. The mass carried by the astronaut is 10.0 kg, in two packages of 5 kg each. Step 2 of 8 The expression to find the velocity in space is, Here, is exhaust velocity, is initial mass, is initial velocity and is remaining mass Now, the remaining mass is: Hence, the remaining mass is 70.0kg Substitute, for , for and for , Hence , the velocity of astronaut toward the spaceship in space is v= 0.401 m/s. Step 3 of 8 The expression to find the time required to reach the spaceship is: Substitute for and for in the expression of time. Hence the time taken by astronaut to reach to the spaceship is . Step 4 of 8 If she expels the packages in parts then the time required is: Now, consider she put the mass out is 5.00 kg in two parts. So, for the first part, The remaining mass is: Substitute for , for , 0 m/s for and for in the expression of velocity written above and calculate . Now, for this, if the half distance is travelled, then the time required is: Hence, the time required to expels the packages in parts is 25.8s.