you are increasing speed by (20/15)
power= 100hp (20/15)^3
power= 100hp (20/15)^3
According to the problem, we know that P is directly proportional to the cube of the speed:
P ∝ s^3
Let's introduce a constant of proportionality, k, to represent the ratio between P and s^3:
P = k * s^3
We also know that a 100 hp engine is needed to propel the boat at 15 knots. We can use this information to find the value of k.
Plugging in the values for P and s into the equation, we have:
100 = k * 15^3
Simplifying, we have:
100 = k * 3375
Now, we can solve for k by dividing both sides of the equation by 3375:
k = 100 / 3375
k = 0.02963
Now that we have the value of k, we can find the power needed to drive the boat at 20 knots. Let's plug in the value of s into the equation:
P = 0.02963 * 20^3
Simplifying, we have:
P = 0.02963 * 8000
P ≈ 237
Therefore, the power needed to drive the boat at 20 knots is approximately 237 hp.
The problem states that the power P needed to propel a boat is directly proportional to the cube of the speed of the boat.
Let's assume that P represents the power needed and S represents the speed of the boat.
According to the problem, we can write the equation as follows:
P = k * S^3
Where k is the constant of variation.
We are given that a 100 hp engine is needed to propel the boat at 15 knots, so we can substitute these values into the equation:
100 = k * (15^3)
To solve for k, divide both sides of the equation by (15^3):
k = 100 / (15^3)
Now we can use the value of k to find the power needed to drive the boat at 20 knots.
P = k * (20^3)
Substituting the value of k, we have:
P = (100 / (15^3)) * (20^3)
Simplifying the equation:
P = (100 / 3375) * 8000
P ≈ 237.04 hp
Therefore, the power needed to drive the boat at 20 knots is approximately 237.04 hp.