(a)

Ship A is 150 km west of ship B.

Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h.

(b)

Rate at which distance between two ships is changing at 4:00 Pm.  

(c)

At any time :

Consider horizontal distance traveled by the ship A is  .

Consider the vertical distance traveled by the ship B is  .

Consider the distance between the ships is .

Diagram of the situation at any time .

(d)

From the above figure, 

Apply Pythagorean theorem to the above diagram.

.

Differentiate on each side with respect to .

(e)

Ship A is sailing east at 35 km/h.

Therefore, km/h.

Ship B is sailing north at 25 km/h.

Therefore, km/h.

Rate at which distance between two ships changing at any time is .

Find the distance traveled by ship A in 4 hours is .

Distance= speed time.

Find the distance traveled by ship B in 4 hours is .

Find the distance between the ships at 4.00 PM.

.

Substitute and in above expression.

Consider the result in part (d) .

Substitute corresponding values in above expression.

Rate at which distance between two ships changing at 4:00 Pm is km/h.

(a)

Ship A is 150 km west of ship B.

Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h.

(b) Rate at which distance between two ships is changing at 4:00 PM. 

(c)

(d) .

(e) Rate at which distance between two ships changing at 4:00 PM is km/h.