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- Homework Statement
- A small rock moves in water and the force exerted on it by the water is given by f = kv.

The terminal speed of the rock is 2.00 m/s, and the rock is projected upward at an initial speed of 6.00 m/s. Ignore the bouyancy force on the rock.

a.) Without fluid resistance, how high will the rock rise & how long does it take to reach this maximum height?

b.) When fluid resistance is included, what are the answers to the question in part (a)?

- Relevant Equations
- 1.) f = kv

2.) v_y(t) = v_t * (1 - exp(-kt/m)) + v_0(exp(-kt/m))

3.) y(t) = v_t*t + m/k*exp(-kt/m)*(v_t - v_0)

Good evening,

I have a question on the problem I've provided in the homework statement. Essentially, the problem is asking us to compare the maximum height and time to max-height between a simple projectile motion case vs. a case using fluid resistance proportional to v. I've solved everything correctly and my answers match the solution in the back of my book, but there's something odd I can't seem to wrap my head around.

In the simple projectile motion case with no fluid resistance, the rock starts at y = 0 and climbs to a maximum height of 1.84m in 0.612 seconds using basic kinematics equations. No problem there.

When fluid resistance is involved, I integrated the 2nd equation to get the 3rd, using t = 0 to the time of max-height of 0.283s. The details involving that process aren't too important here since it's correct, but this is what I found a little confusing:

At t = 0 using equation 3, I get an initial starting point of y = 1.63m. (Positive, because in part B I set the downward direction to +y)

Is there a reason that the rock is displaced 1.63m away from y = 0 when fluid resistance is included at the beginning time? Seems a little strange that the rocks wouldn't both start at y = 0. Instead, when fluid resistance turns on, the rock starts from a much lower position despite not having any time to move compared to the basic projectile motion version.

Hopefully that makes sense. Thank you for your input.

I have a question on the problem I've provided in the homework statement. Essentially, the problem is asking us to compare the maximum height and time to max-height between a simple projectile motion case vs. a case using fluid resistance proportional to v. I've solved everything correctly and my answers match the solution in the back of my book, but there's something odd I can't seem to wrap my head around.

In the simple projectile motion case with no fluid resistance, the rock starts at y = 0 and climbs to a maximum height of 1.84m in 0.612 seconds using basic kinematics equations. No problem there.

When fluid resistance is involved, I integrated the 2nd equation to get the 3rd, using t = 0 to the time of max-height of 0.283s. The details involving that process aren't too important here since it's correct, but this is what I found a little confusing:

At t = 0 using equation 3, I get an initial starting point of y = 1.63m. (Positive, because in part B I set the downward direction to +y)

Is there a reason that the rock is displaced 1.63m away from y = 0 when fluid resistance is included at the beginning time? Seems a little strange that the rocks wouldn't both start at y = 0. Instead, when fluid resistance turns on, the rock starts from a much lower position despite not having any time to move compared to the basic projectile motion version.

Hopefully that makes sense. Thank you for your input.