Question

An 80.0kg skydiver jumps out of a balloon at an altitude of 1 000 m and opens his parachute at an altitude of 200 m. (a) Assuming the total retarding force on the skydiver is constant at 50.0 N with the parachute closed and constant at with the parachute open, find the speed of the skydiver when he lands on the ground. (b) Do you think the skydiver will be injured? Explain. (c) At what height should the parachute be opened so that the final speed of the skydiver when he hits the ground is 5.00 m/s? (d) How realistic is the assumption that the total retarding force is constant? Explain.

Short answer

(a) The speed of the skydiver when he lands on the ground is 24.5m/s

Step-by-step solution

Step-by-step-solutionStep 1:

If the system is isolated, total energy remains constant.

$△E_{system}=0$

which can be written as:

$△K+△U+△E_{int}=0$

Ifnon-conservative forces are present, the mechanical energy of the system remains constant.

$△E_{mech}=0$

which can be written as:

Given data

Skydiver’s mass: m=80Kg

Altitude at which he jumps: y=1000m

Altitude at which parachute is opened:h=200m

Retarding force when the parachute is closed:f₁=50N

Retarding force when the parachute is open:f₂=3600N

Step 3:Part-(a)

From step (1), the air drag does work which is equal to a change in mechanical energy; we have