. An alligator wishes to swim north, directly across a channel 500 m wide. There is a
current of 2.5 m/s flowing east. The alligator is capable of swimming at 4.0 m/s. What is
the angle at which the alligator must point its body in order to swim directly across the
channel?
a. 35° W of N
b. 37° W of N
c. 39° W of N
d. 41° W of N
To find the angle at which the alligator must point its body in order to swim directly across the channel, we need to use vector addition.
Let the direction the alligator is aiming to go be north. The current is flowing east, so its velocity is 2.5 m/s to the east. The alligator's velocity is 4.0 m/s to the north.
To find the angle, we can use the tangent of the angle with respect to the north direction:
tan(θ) = (current velocity) / (alligator velocity)
tan(θ) = 2.5 / 4.0
tan(θ) = 0.625
Now, we need to take the arctan of 0.625 to find the angle:
θ = arctan(0.625)
θ ≈ 32.7°
So, the angle at which the alligator must point its body is approximately 32.7° west of north.
Since 32.7° is not an option, the closest option is 35° W of N, which would be the correct answer.