Question

A boat crosses a river of width 115 m in which
the current has a uniform speed of 1.84 m/s.
The pilot maintains a bearing (i.e., the direction
in which the boat points) perpendicular
to the river and a throttle setting to give a
constant speed of 1.1 m/s relative to the water.
What is the magnitude of the speed of the
boat relative to a stationary shore observer?
Answer in units of m/s.

How far downstream from the initial position
is the boat when it reaches the opposite shore?
Answer in units of m.

Answer 1

X = 1.84 m/s = Velocity of the current.
Y = 1.1 m/s = Velocity of the boat.

A. Vb^2 = X^2 + Y^2 = 1.84^2 + 1.1^2 =
4.60
Vb = 2.14 m/s.

B. Tan A = Y/X = 1.1/1.84 = 0.59783
A = 30.9o, CCW = 59.1o E. of N.

Tan59.1 = d/115
d = 115*Tan59.1 = 192 m. Downstream.