Question

A boat's motor propels the boat through the water at 3m/s. The driver of the boat wants to go in a straight ine directly across the river, but there is a 1m/s current flowing perpendicular to the direction in which the driver wants to go

Answer 1

Direction of boat's motion = 109.52°

Step-by-step explanation:

In the question,

Speed of the boat, v = 3 m/s

Speed of the current, c = 1 m/s

The speed of the current is perpendicular to the resultant direction of the motion of the boat, R.

So,

In the triangle, using the Pythagoras Theorem,

`v^(2)=c^(2)+R^(2)`

So,

`(3)^(2)=1^(2)+R^(2)\\R^(2)=8\\R=2√(2)\\R=2.828\,m/s`

Therefore, the Resultant speed of the Boat is given by,

R = 2.82 m/s

And,

Direction of the motion of the Boat is given by,

`tan\theta=(c)/(R)\\tan\theta=(1)/(2.82)=0.354\\\theta=19.52\,degrees`

So,

Angle made by the Boat with the Horizontal is,

θ = 90 + 19.52 = 109.52°

Therefore, the Boat should be moving at 109.52° with the horizontal.