If the skydiver's daughter, whose mass is 4545 kg, is falling through the air and has the same DD (0.250.25 kg/m) as her father, what is the daughter's terminal speed?

Ch 05: Applying Newton's Laws

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

All textbooks

Young & Freedman Calc 14th Edition

Ch 05: Applying Newton's Laws

Problem 42b

Chapter 5, Problem 42b

If the skydiver's daughter, whose mass is $45$ kg, is falling through the air and has the same $D$ ( $0.25$ kg/m) as her father, what is the daughter's terminal speed?

Verified step by step guidance

Identify the forces acting on the skydiver's daughter: The two main forces are gravitational force (weight) and air resistance. At terminal velocity, these forces are balanced, meaning the net force is zero.

Write the equation for terminal velocity: At terminal velocity, the gravitational force (mg) is equal to the drag force (1/2 * D * A * v^2), where m is the mass, g is the acceleration due to gravity, D is the drag coefficient, A is the cross-sectional area, and v is the terminal velocity.

Rearrange the equation to solve for terminal velocity (v): Start with mg = (1/2) * D * A * v^2. Rearrange to isolate v: v = sqrt((2 * m * g) / (D * A)).

Substitute the known values into the equation: Use m = 45 kg, g = 9.8 m/s^2, and D = 0.25 kg/m. Note that the cross-sectional area (A) is not provided in the problem, so you will need to assume it is the same as the father's or use a reasonable estimate.

Simplify the expression to find the terminal velocity: Perform the necessary algebraic operations to compute the terminal velocity, ensuring all units are consistent.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

58s

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Terminal Velocity

Terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration. At this point, the force of gravity is balanced by the drag force acting against it, resulting in a net force of zero.

Drag Coefficient (D)

The drag coefficient (D) is a dimensionless number that quantifies the drag or resistance of an object in a fluid environment, such as air. It depends on the shape of the object and the flow conditions, and it plays a crucial role in determining the drag force experienced by the object as it moves through the fluid.

Mass and Weight

Mass is a measure of the amount of matter in an object, typically measured in kilograms, while weight is the force exerted by gravity on that mass. Weight can be calculated using the formula W = mg, where W is weight, m is mass, and g is the acceleration due to gravity (approximately 9.81 m/s² on Earth).

Recommended video:

Guided course

10:19

Torque Due to Weight

Related Practice

Textbook Question

Two crates connected by a rope lie on a horizontal surface (Fig. E $5.37$ ). Crate A has mass $m_A$ , and crate B has mass $m_B$ . The coefficient of kinetic friction between each crate and the surface is $μ_k$ . The crates are pulled to the right at constant velocity by a horizontal force $F$ . Draw one or more free-body diagrams to calculate the following in terms of $m_A$ , $m_B$ , and $μ_k$ : the tension in the rope connecting the blocks.

views

Textbook Question

A $52$ -kg ice skater spins about a vertical axis through her body with her arms horizontally outstretched; she makes $2.0$ turns each second. The distance from one hand to the other is $1.50$ m. Biometric measurements indicate that each hand typically makes up about $1.25 percent sign$ of body weight. What horizontal force must her wrist exert on her hand?

views

Textbook Question

You throw a baseball straight upward. The drag force is proportional to $v^2$ . In terms of $g$ , what is the $y$ -component of the ball's acceleration when the ball's speed is half its terminal speed and it is moving back down?

views

Textbook Question

A small remote-controlled car with mass $1.60$ kg moves at a constant speed of $v equals 12.0$ m/s in a track formed by a vertical circle inside a hollow metal cylinder that has a radius of $5.00$ m (Fig. E $5.45$ ). What is the magnitude of the normal force exerted on the car by the walls of the cylinder at point $A$ (bottom of the track)?

views

Textbook Question

A small remote-controlled car with mass $1.60$ kg moves at a constant speed of $v = 12.0$ m/s in a track formed by a vertical circle inside a hollow metal cylinder that has a radius of $5.00$ m (Fig. E $5.45$ ). What is the magnitude of the normal force exerted on the car by the walls of the cylinder at point $B$ (top of the track)?

views

Textbook Question

You throw a baseball straight upward. The drag force is proportional to $v^{2}$ . In terms of $g$ , what is the $y$ -component of the ball's acceleration when the ball's speed is half its terminal speed and it is moving up?

views