Math problem...plzzzzzz help?

Question

While floating down a river with a 2.75 mi/hr current, Alicia decides
to swim toward the river bank. She can swim 0.75 mi/hr in still water.
What is the actual speed at which she moves toward the bank? At what
angle will she approach the bank, measured with respect to the bank?

Answer 1

Assuming she is swimming perpendicular to the flow of the river, then you can set up a right triangle. In one hour, the current (1 leg of your triangle) moves 2.75 miles; in that same answer, Alicia (the other leg) moves 0.75 miles towards the bank.

You can use those to figure out the angle she's approaching the bank. Call that angle X.
Tangent = opposite / adjacent
tan(X) = 2.75 / 0.75 = 3 2/3.

X = arctan(3 2/3) = 74.74 degrees with respect to the adjacent leg, so that would be 90-74.74 = 15.26 degrees with respect to the bank.

Hope that helps.

Answer 2

You have two vector quanties, current and the swimming speed. If Alicia is swimming perpendicular to the river current, the velocity due to both effects is found from Phyagroean Theorum:
real velocity= sqrt ( current**2+swim velocity**2)

The angle she approaches the bank is the an angle theta such that
Cosine (theta) = current velocity/real velocity.

You can plug in the values and crank it out.

Answer 3

Since there is no component of river current towards or away from the bank, her approach to the bank will be 0.75 mph. The angle at which she approaches the bank will be atan(0.75/2.75) ≈ 15.255° Her speed towards her landing point will be 2.75/cos(15.255°) ≈ 2.85 mph.

Answer 4

Eh... neither... yet i assume i'm going to choose English. I used to love English greater yet severe college made it boring. -_- yet I nonetheless love writing as a activity (and hate math, even however i'm no longer undesirable at it) so i'm going to purely say English.