How Do You Calculate the Direction of a Child Walking on a Moving Ship?

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A child walking due east at 1 mph on a ship moving north at 1 mph has a resultant speed of sqrt(2) mph relative to the water. The child's eastward speed remains 1 mph, while the northward speed is also 1 mph, resulting in a vector speed of <1,1>. To find the direction, one can visualize this as a right triangle, where the angle can be calculated using trigonometric functions. The angle from the north can be determined based on the known components of the vector. This approach effectively combines the child's and ship's movements to calculate the overall direction and speed.
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A child walks due east on the deck of a ship at 1 miles per hour.
The ship is moving north at a speed of 1 miles per hour.

Find the speed and direction of the child relative to the surface of the water.


speed = sqrt(2)

im having trouble finding the direction

The angle of the direction from the north = _____ (radians)

V_c = &lt;1,0&gt;
V_s = &lt;0,1&gt;
V= &lt;0,V&gt;

im not sure how i can find the direction
 
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The reasoning is as follow: The ship's speed is 1mph NORTH relative to water. The child's speed is 1mph EAST relative to the ship. But the ship has eastward speed 0mph. So the child's eastward speed relative to water is 1+0=1mph. Similarily, the child's northward speed relative to water is 0+1mph = 1 mph

So he has an eastward component of 1 and a northward component of 1. Hence is vector speed is <1,1>. Draw this vector and its components. You got yourself a right triangle for which you know 1 angle and 3 sides. It's easy to find the angle giving the direction of the vector speed.
 

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