Sailing north at a speed of 20mph, ship A leaves a port. A half hour later, ship B leaves the same port, sailing East at speed of 25 mph.

Question

Sailing north at a speed of 20mph, ship A leaves a port. A half hour later, ship B leaves the same port, sailing East at speed of 25 mph. Let t (hours) denote the time B has been at the sea.

1. find an expression in terms of t that gives the distance D between the two cargo ships
2. use the expression obtained in part (1) to find the distance between two cargo ships 3 hours after ship A has left the port

Answer 1

Sa T

Let's find the coordinates of ships A, B at time t.

As A is sailing north, x coordinate will always be 0, y will be 20t so (0,20t)

As B is sailing east, y coordinate will always be 0, so (25t , 0)

You can use the distance formula to find the distance between them. Take the difference in the x coordinates, square, take the difference in the y coordinates, square, add these two squares together and take the square root. That will give your expression in (1).

Then substitute t=3 to solve part 2.

Mike