A child walks due east on the deck of a ship at 5 kilometers per hour. The ship is moving north at a speed of 30 kilometers per hour. Find the speed and direction of the child relative to the surface of the water. (a) Speed = ?_ km/h (b) The angle of the direction is ?radians. Note : Traditionally north is 0 degrees so 0 rad, east is 90 degrees so (pi2) rad, south is 180 degrees so pi rad and west is 270 degrees or ((3pi)/2) rad.

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(a) The speed can be found using the Pythagorean theorem. Since North is orthoganal to East we have the speed as the hypotenuse of a right triangle with legs 30 and 5.

`(sp)^2=30^2+5^2==>sp=sqrt(925)=5sqrt(37)~~30.4 "km"/"hr"`

(b) We can find the angle using the right triangle. If `theta` is the angle measured off the leg running North/South we have:

`tantheta=5/30 ==> theta=tan^(-1)(1/6)~~.165` radians East of North.

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