Question

A child walks due east on the deck of a ship at 3 miles perhour.

The ship is moving north at a speed of 16 miles per hour.
Find the speed and direction of the child relative to thesurface of the water.
Speed = mph
The angle of the direction from the north = (radians)

Answer 1

16.28 mph ; 79.38°

Explanation:

Given the following :

Speed of child due east = 3mph

Speed of ship due North = 16mph

Relative speed of th child is obtained by using Pythagoras rule to find the hypotenus

Relative Speed = Sqrt(3² + 16²)

Relative Speed = sqrt(9 + 256)

= sqrt(265)

= 16.2788 mph

= 16.28 mph

From trigonometry ;

Tanθ = opposite / Adjacent

Tanθ = (16 / 3)

Tanθ = 5.333

θ = tan^-1(5.333)

θ = 79.379°

θ = 79.38°