Question

Two ships leave the same port at noon. Ship A sails north at 14 mph, and ship B sails east at 17 mph. How fast is the distance between them changing at 1 p.m.? (Round your answer to one decimal place.)

Answer 1

Step 1)

Let's assume that,

x = distance from port to ship A

y = distance from port to ship B

Two ships leave the port at noon means at 12:00 pm

Ships A sails north at 14 mph means dx/dt = 14 and hence it sails 14 miles in one hour means at 1 pm distance between port and ship A is x = 14*1 = 14 miles

Ships B sails east at 17 mph means dy/dt = 17 and hence it sails 17 miles in one hour means at 1 pm distance between port and ship B is y = 17*1 = 17 miles

we can graph the mathematical problem as below :

According to Pythagoras theorem we can write distance between two ships is given by,

we have x = 14 and y = 17 hence,

we have,

differentiate both the side with respect to t we can write,

we have,

rounding to one decimal place we can say that,

Hence we can say that at 1 pm distance between two ships is changing at a rate of 22 mph