Calculate Drag Coefficient for Jumpers

How do we calculate the drag coefficients for the jumpers?

Given the masses and velocities of the two jumpers, how can we determine the drag coefficients they experience?

Answer:

To calculate the drag coefficients for the jumpers, we need to first calculate the drag forces acting on each jumper. This can be done by determining the acceleration of the jumpers using kinematic equations of linear motion.

Once we have the drag forces, we can then calculate the drag coefficients by dividing the drag force by the velocity of the jumpers.

When analyzing the scenario with the first jumper weighing 85 kg and the second jumper weighing 60 kg, both jumping from the same level with an initial velocity of 0 and reaching a velocity of 20 m/s in 6 seconds, we can proceed with the following calculations.

First, we find the acceleration experienced by the jumpers using the formula:

Acceleration (a) = Change in velocity / Time taken = 20 m/s / 6 s = 3.33 m/s^2

Next, we calculate the drag forces for each jumper:

Drag force for first jumper (F_u1) = Mass of first jumper x Acceleration = 85 kg x 3.33 m/s^2 = 283.05 N

Drag force for second jumper (F_u2) = Mass of second jumper x Acceleration = 60 kg x 3.33 m/s^2 = 199.8 N

With the drag forces determined, we can now calculate the drag coefficients:

Drag coefficient for first jumper (C_1) = - Drag force for first jumper / Velocity = -283.05 N / 20 m/s = -14.1525

Drag coefficient for second jumper (C_2) = - Drag force for second jumper / Velocity = -199.8 N / 20 m/s = -9.99

Therefore, the drag coefficient for the first jumper is approximately -14.1525 and for the second jumper is approximately -9.99.