Question

A motorboat with a speed of 9 mph in still water must aim upstream at an angle of 25.5 degrees in order
to travel directly across the stream. What is the speed of the current? What is the resultant speed of the
boat?

Answer 1

Given:

Let speed of boat be V = 9 mph

Boat aims upstream at an angle 25.5 degrees

To find:

We have to find the resultant speed of the boat

Solution:

Refer to the attached wofd file for diagram

$V_c$ = Velocity of current

$V_r$ = Resultant Velocity of Boat

We get,

$V_c$  = $(sin25.5)(V)$

    = $(sin25.5)(9)$

$V_c$  = 3.874 mph

And we got,

$V_r$ = $(cos 25.5)(V)$

    = $(cos 25.5)(9)$

$V_r$ = 8.12 mph

∴ The speed of the current is 3.874 mph.

∴ The resultant speed of the boat is 8.12 mph.