A child and parent parachute jump together. Assume that the parent is heavier than the child. The following questions will ask you about different aspects of their trip down.
A. Before they open their parachutes, both the parent and the child fall with the same acceleration and velocity. How does the total force acting on the child compare to the total force acting on the parent? Explain your reasoning!
B. Once they open their parachutes, in addition to gravity they also feel the force of the parachute ropes pulling on them. Soon after their parachutes are opened, they are no longer accelerating or decelerating, but instead fall at a uniform velocity. What is the total force on the parent and the total force on the child during the time they are falling at a uniform velocity?
C. How does the force exerted by the parachute on the child compare to the force exerted by the parachute on the parent if they continue to fall together next to each other?

Before opening the parachute the drag force is negligible and so their velocity and acceleration are same simultaneously. The total force acting on the child is lesser than the total force of gravity on the child because the force of gravity is given as:

[tex]F=m.g[/tex]

where:

m= mass

g= acceleration due to gravity

So when the mass is greater then the force of gravity is also greater on the body.

B

During the uniform velocity motion there is no acceleration in the body and hence we can say the there is no net force acting on the body.

The net force acting on the body is zero.

C

The force of drag acts due to parachute on each of the body when falling with uniform motion, this drag force is equal to the force of gravity acting on each of them individually.

So the drag force on the heavier body is greater than the drag force on the lighter body. During this condition the bodies fall with a uniform velocity called terminal velocity.

[tex]m.g=\frac{1}{2}\rho.A.v^2.c_d[/tex]

where:

[tex]\rho=[/tex] density of the air

A= area normal to the direction of fall

v= terminal velocity

[tex]c_d=[/tex] coefficient of drag