Final answer:
The power needed to row a boat at a certain speed is proportional to the square of that speed. Therefore, when the speed of a boat is doubled, the required horsepower increases fourfold, resulting in 96 h.p. for a boat originally requiring 24 h.p. at half the final speed.The correct option is option c .
Step-by-step explanation:
The question asks about the relationship between the force required to power a boat and the boat's speed, using horsepower (h.p.) as a measure of the required force. Given that 24 h.p. is needed to row a boat at 8 km/hr, and knowing that the force required to row a boat over the sea is proportional to the square of the speed of the boat, we can calculate the horsepower required when the speed is doubled.
First, let's establish the proportionality between force (power) and the square of the speed. If P represents power and v represents speed, then P is proportional to v^2. We know that P1 = 24 h.p. at v1 = 8 km/hr, so when the speed v is doubled (v2 = 16 km/hr), the power P2 needed can be calculated by the ratio:
P1/P2 = (v1^2)/(v2^2)
P2 = P1 * (v2/v1)^2
P2 = 24 h.p. * (16/8)^2
P2 = 24 h.p. * 4 = 96 h.p.
Therefore, when the speed of the boat is doubled from 8 km/hr to 16 km/hr, the horsepower required also increases by a factor of four, resulting in 96 h.p.