   Chapter 5, Problem 49P

Chapter
Section
Textbook Problem

An 80.0-kg skydiver jumps out of a balloon at an altitude of 1.00 × 103 m and opens the parachute at an altitude of 200.0 m. (a) Assuming that the total retarding force on the diver is constant at 50.0 N with the parachute closed and constant at 3.60 × 103 N with the parachute open, what is the speed of the diver when he lands on the ground? (b) Do you think the skydiver will get hurt? 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.

(a)

To determine
The speed of the diver when he lands on the ground.

Explanation

Given Info:

The mass of the sky diver is 80.0kg .

The height of the balloon from which the sky diver jumps is 1.0×103m .

The parachute opens at an altitude of 200.0m .

The total retarding force when the parachute is open is 50.0N .

The total retarding force when the parachute is closed is 3.60×103N .

According to the Work-Energy theorem in the entire trip,

Wnc=(KE+PEg)f(KE+PEg)i

Since, the retarding force is opposite to the motion of the diver and the final potential energy and initial kinetic energy of the diver is zero. Because the diver is starting from rest and the final position is to the ground.

(F1cos180°)d1+(F2cos180°)d2=(12mvf2+0)(0+mghi)

• F1 is the total retarding force when the parachute is open
• F2 is the total retarding force when the parachute is closed
• d1 is the distance that the diver travels with closed parachute
• d2 is the height from which the parachute is open
• m is the mass of diver
• hi is the initial height of the diver
• vf is the speed of the diver when he lands on the ground

On re-arranging,

Formula to calculate speed of the diver when he lands on the ground is,

vf=2(ghiF1d1+F2d2m)

Substitute 9

(b)

To determine
Whether the skydiver will get hurt.

(c)

To determine
The height with which the parachute should be opened if he needs a landing speed of 5.0m/s

(d)

To determine
how realistic is the assumption that the total retarding force is a constant.

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