An astronaut finds herself in a predicament in which she has become untethered from her shuttle. she figures that she could get back to her shuttle by throwing one of three objects she possesses in the opposite direction of the shuttle. the masses of the objects are 5.3 kg, 7.9 kg, and 10.5 kg, respectively. she is able to throw the first object with a speed of 15.00 m/s, the second with a speed of 11.2 m/s, and the third with a speed of 7.0 m/s. if the mass of the astronaut and her remaining gear is 75.0 kg, determine the final speed of the astronaut with respect to the shuttle if she were to throw each object successively, starting with the least massive and ending with the most massive. assume that the speeds described are those measured in the rest frame of the astronaut.

In order to solve the problem, it is necessary to apply the concepts related to the conservation of momentum, especially when there is an impact or the throwing of an object.

The equation that defines the linear moment is given by

where,

m=Total mass

Mass of Object

Velocity before throwing

Final Velocity

Velocity of Object

Our values are:

Solving to find the final speed, after throwing the object we have

We have three objects. For each object a launch is made so the final mass (denominator) will begin to be subtracted successively. In addition, during each new launch the initial speed will be given for each object thrown again.

That way during each section the equations should be modified depending on the previous one, let's start:

A)

B)

C)

Therefore the final velocity of astronaut is 3.63m/s

here we know that ball will drop down by total distance 3.2 m

so here we know that

now using kinematics

now in the same time it will cover horizontal distance of 0.75 m

so speed of the ball will be

small = small current large mag large current