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

Answer:

Direction of boat's motion = 109.52°

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,

$(3)^{2}=1^{2}+R^{2}\\R^{2}=8\\R=2\sqrt{2}\\R=2.828\,m/s$

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,

$tan\theta=\frac{c}{R}\\tan\theta=\frac{1}{2.82}=0.354\\\theta=19.52\,degrees$

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.