Question

A river flows due east at 12 km/h. A boat crosses the 720 m wide river by maintaining a constant velocity of 72 mi/h due north relative to the water. If no correction is made for the current, how far downstream does the boat move by the time it reaches the far shore?

Answer 1

Answer:

The boat will be 74 .17 meters downstream by the time it reaches the shore.

Explanation:

Consider the vector diagrams for velocity and distance shown below.

converting 72 miles per hour to km/hr

we have 72 miles per hour 72 × 1.60934 = 115.83 km/hr

The velocity vectors form a right angled triangle, and can be solved using simple trigonometric laws

$tan \theta = \frac{12}{115.873}$

$\theta = tan^{-1}( \frac{12}{115.873})=5.9126$

This is the vector angle with which the ship drifts away with respect to its northward direction.

From the sketch of the displacement vectors,  we can use trigonometric ratios to determine the distance the boat moves downstream.

Let x be the distance  the boat moves downstream.d

$sin(5.9126)=\frac{x}{720}$

$x= 720\times 5.9126$

$x=74.17m$

∴The boat will be 74 .17 meters downstream by the time it reaches the shore.