Answer :
Final answer:
Using Newton's second law, the average force exerted on the dolphin, which is decelerating horizontally, is calculated by finding the change in velocity, dividing by time to find acceleration, and then multiplying by the dolphin's mass. The calculated force is 78.12 N, which does not match the provided answer choices, possibly indicating a typo in the question or answers.
Explanation:
Average Force Exerted on a Decelerating Dolphin
To calculate the average force exerted on a 36 kg dolphin that decelerates from 12.5 m/s to 7.5 m/s over a time period of 2.3 seconds, we will apply Newton's second law of motion.
Newton's second law states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration (F = ma). Here, acceleration can be found using the formula for acceleration (a) which is the change in velocity (Δv) divided by the change in time (Δt). The change in velocity is the final velocity minus the initial velocity. Apply these values to find the acceleration:
Δv = final velocity - initial velocity = 7.5 m/s - 12.5 m/s = -5.0 m/s
a = Δv / Δt = -5.0 m/s / 2.3 s = -2.17 m/s²
Now multiply the mass of the dolphin (m = 36 kg) by the found acceleration (a = -2.17 m/s²) to get the force (F):
F = m * a = 36 kg * -2.17 m/s² = -78.12 N
The negative sign indicates that the force is acting opposite to the dolphin's direction of motion, which makes sense since it is decelerating. Since force can't be negative, we take the absolute value: |F| = 78.12 N.
Looking at the options provided in the question, none of them match our calculation exactly. Therefore, it is reasonable to assume that there might be a typo in the question or answer choices. However, in practice, one would select the closest answer: b) 52 N, which is still not correct based on our calculations. Always verify the values provided in the multiple choices against the calculated result before selecting the closest answer.
