Question

You want to paddle a boat straight across the Mississippi River. You are able to paddle the boat with a speed of 2.2 m/s relative to the water, and the current flows at a speed of 1.1 m/s. In what direction (angle), relative to the river bank, do you need to point the boat to cross the river in the shortest time? The width of the river is 95.0 m.

A) 60 degrees
B) 80 degrees
C) 90 degrees
D) 70 degrees
E) 50 degrees

Answer 1

C) 90 degrees

Step-by-step explanation:

If we could have an imaginative illustration about what the question is all about.

We could think of the velocity of the river (V_r cosθ) as a horizontal component and the velocity of the boat (V_b sinθ) as the vertical component.

So the velocity of the boat V_b = 2.2 m/s; &

the velocity of the river V_r = 1.1 m/s

∴

The minimum time (which is the shortest time) required for the boat to cross the river is θ = 90°

the time require is:

`t = (d)/(v_b \ sin \theta)`

`t = (95)/(2.2)`

t = 43.18 sec