Chapter 4, Problem 48A

(a)

To determine

To Describe: what happens to skydiver’s velocity as she opens the parachute.

Answer to Problem 48A

As the skydiver opens her parachute there will be a sudden drop in her velocity.

Explanation of Solution

Introduction:

Skydiving is a sport where a skydiver jumps from an airplane and carries out a number of gymnastic exercises before tugging the parachute chord. The principle of physics which governs the process of skydiving consists of the interaction between the air resistance and the acceleration due to gravity. As soon as a skydiver jumps out of an airplane, he/she starts accelerating in downward direction, up till he/she reaches the terminal speed. Terminal speed of a skydiver is a speed at which there will be a balance between the force due to air resistance and the force due to gravity dragging him/her down.

As the skydiver opens her parachute, there will be a sudden drop in her velocity. This is because, when the parachute opens, it covers a large surface area which leads to increase in air resistance acting on the total mass (skydiver + parachute). Increase in air resistance reduces the velocity of a skydiver sufficient for her to land without getting any harm.

Conclusion:

As the skydiver opens her parachute, there will be a sudden drop in her velocity.

(b)

To determine

To Describe: The skydiver’s velocity from when her parachute has been open for a time until she is about to land.

Answer to Problem 48A

Once the skydiver opens her parachute, force of air resistance and gravitational force becomes equal and hence the skydiver continues downwards with a constant velocity.

Explanation of Solution

Introduction:

When a skydiver jumps out of an airplane there are two forces acting on her: The Earth’s gravitational force pulling her straight down, and the air resistance. Air resistance pushes the skydiver in the upward direction. Air resistance increases as the skydiver’s speed increases. Thus, when a skydiver starts dropping from a plane and moving slowly, gravitational force is stronger than the air resistance and she speeds up and accelerates towards the Earth. As she is moving faster, air resistance acting on her also increases and slows down her velocity.

Once the skydiver opens her parachute, the air resistance acting on her increases and there will be a sudden drop in her velocity. Now the force of air resistance become equal to that of gravitational force. Since the air resistance is acting in upward direction (opposing the downward motion of the skydiver) and the gravitational force is in the downward direction (accelerating the skydiver towards the earth), their sum becomes zero. So, the skydiver will not accelerate any more. And hence the skydiver continues downwards with a constant velocity so that she lands safely.

Conclusion:

Once the skydiver opens her parachute, force of air resistance and gravitational force becomes equal and hence the skydiver continues downwards with a constant velocity.