Terminal Velocity and Resistive Forces problem

[cheese825]

Homework Statement

A sky diver of mass 81.5 kg jumps from a slow-moving aircraft and reaches a terminal speed of 50.0 m/s.
(a) What is the acceleration of the sky diver when her speed is 30.0 m/s?

Homework Equations

mg = bv
where b is the friction constant
and v is the terminal velocity

The Attempt at a Solution

b = (81.5)(9.8) / 50
b = 15.97

(81.5)(9.8) - (15.97)(30) = remaining force, or 319.6 Newtons
319.6 N / 81.5 = 3.921

but it seems, 3.921 is not correct. I must be missing something big.
Any help would be appreciated.

 

[Hootenanny]

A number of things could cause your answer to be off.

Firstly, if you are entering your answers online be careful with your significant figures - online marking software can be very pedantic about such things.

Secondly, were you explicitly told that the drag force was a linear function of velocity because for large objects moving faster than a few m/s the drag force is usually a quadratic function of velocity.

 

[thomate1]

Your attempt at a solution is on the right track, but there are a few errors in your calculations. Let's break down the problem and go through it step by step.

First, we are given the mass of the sky diver (81.5 kg) and the terminal speed (50.0 m/s). We can use this information to calculate the friction force (F) acting on the sky diver at terminal velocity using the equation F = bv, where b is the friction constant.

F = bv
F = (81.5 kg)(9.8 m/s^2)
F = 798.7 N

Next, we are asked to find the acceleration of the sky diver when her speed is 30.0 m/s. This means that the friction force is no longer equal to the force of gravity (mg), since the sky diver is not at terminal velocity. We can use the equation F = ma to find the acceleration (a).

F = ma
798.7 N = (81.5 kg)a
a = 9.8 m/s^2

So, the acceleration of the sky diver when her speed is 30.0 m/s is 9.8 m/s^2. This is the same as the acceleration due to gravity, which makes sense since the sky diver is no longer experiencing any other forces.

In your attempt at a solution, you calculated the friction constant (b) using the equation mg = bv. This is not correct, as the equation should be mg = bv^2. Additionally, when you used the equation F = ma, you did not include the force of gravity (mg) in your calculation. This is why you got a different answer than the correct acceleration of 9.8 m/s^2.

I hope this helps clarify the problem and your solution. Remember to always double check your equations and units when solving physics problems. Good luck with your studies!