The drag force F (in pounds) of water on a swimmer can be modeled by F = 1.35s^2 where s is the swimmer’s speed ( in miles per hour). At what speed is the force minimized? **Note** ^ means "to the power of."
Ah, the notorious drag force of water on swimmers. You know, swimming against the forces of nature can be quite challenging, just like trying to swim in a pool full of rubber duckies. Anyway, let's solve your question.
To find the minimum force, we need to find the minimum value of F. We can start by taking the derivative of the function F with respect to s, and then we'll set it equal to zero. Are you ready? Here it goes:
F = 1.35s^2
Let's find the derivative of F with respect to s:
dF/ds = 2(1.35)s^(2-1)
= 2.7s
Now, we set the derivative equal to zero and solve for s:
2.7s = 0
Divide both sides by 2.7, and we get:
s = 0
Huh, that's odd. It seems like the force is minimized at a speed of zero miles per hour. It looks like the water will be gentlest to you when you're not moving at all. So, maybe it's time to take a break from swimming and just enjoy a good laugh instead.
Remember, laughter is the best exercise for your soul.
To find the speed at which the force is minimized, we need to find the minimum point of the function F = 1.35s^2. This can be determined using calculus.
Step 1: Take the derivative of the function with respect to s.
F' = d/ds (1.35s^2)
= 2 * 1.35 * s^(2-1)
= 2.7s
Step 2: Set the derivative equal to zero and solve for s.
2.7s = 0
Step 3: Divide both sides of the equation by 2.7 to isolate s.
s = 0/2.7
s = 0
Step 4: Interpret the result.
The derivative being zero means the function has a minimum value at s = 0. However, this value does not make sense in the context of the problem since it corresponds to being stationary (not moving). Therefore, there is no minimum force at any positive speed.
In conclusion, the force is not minimized at any speed above zero.
To find the speed at which the force is minimized, we need to differentiate the force equation with respect to the swimmer’s speed (s) and then set the derivative equal to zero. The critical point obtained will give us the minimum force value.
Let's start by differentiating the drag force equation F = 1.35s^2 with respect to s:
dF/ds = 2 * 1.35 * s^(2-1)
Simplifying it further:
dF/ds = 2.7s
To find the critical point, set the derivative equal to zero:
2.7s = 0
We can see that the only solution for this equation is when s = 0.
However, since we're considering the speed of a swimmer, the speed cannot be zero. Therefore, there is no minimum force because the drag force equation does not have a minimum point.
In simple terms, the drag force continuously increases as the swimmer's speed increases, but there is no specific speed where the force is minimized.
stupid question. minimum drag when s=0.
No speed, no drag.
Sure there's not more to the formula?