# Calculus

Boats A and B leave the same place at the same time. Boat A heads due North at 12 km/hr. Boat B heads due East at 18 km/hr. After 2.5 hours, how fast is the distance between the boats increasing?

You are looking at a right-angled triangle, let S be the distance between them

Then S^2 = (12t)^2+(18t)^2=468t^2

then 2S dS/dt = 936t when t-2.5, S = 2925 km

So dS/dt = 936(2.5)/(2x2925) = 0.4 km/h

Actually i figured it. But the correct answer is 21.63 km/hr. Thanks anyways.

of course Mischa, you are right, it looks like I did not take the square root of my S.
Good for you for being alert.

1. š 0
2. š 0
3. š 87

## Similar Questions

1. ### Math

Two boats leave whitby harbour at the same time one boat heads 18 km to it's destination and the other boat heads 11 km to its destination. If the boats headed on a course 70 degrees apart, what is the distance between the boats ?

asked by Aly Baldwin on September 15, 2014
2. ### Math

Two boats leave a dock at the same time. One heads due east at 20 mph, and one heads due south at 15 mph. How far apart are the two boats after 45 minutes have elapsed?

asked by Barb on February 10, 2013
3. ### Calculus

Suppose that two boats leave a dock at different times. One heads due north, the other due east. Find the rate at which the distance between the boats is changing when the first boat is 56 miles from the dock traveling at a speed

asked by Hailey on October 7, 2014
4. ### maths

Two patrol boats M3 and M7 leave port at the same time.M3 heads due west and M7 on a bearing 227 degrees.After 30 minutes M7 has travelled 18 nautical miles and observes M3 in a direction due south.(a)How far is M3 from M7? (b)

asked by Shane on March 8, 2013
5. ### Calculus

At 2:00PM boat X is heading due west at 15mph towards a dock that is exactly 15 miles away. At the same time boat Y leaves the dock traveling due north at a speed of 20mph. At what time will the boats be closest together?

asked by Allison on July 26, 2011
6. ### Math

The position vectors, r km, and velocity vectors, vkm/h, of two boats at a certain time are given by Boat A: 10 am, r(a) = 6i+10j, v(a) = 8i-2j Boat B: 10:30 am, r(b) = 8i+5j, v(b) = 4i+j If the boats collide, find the time when

asked by Joel lu on January 14, 2013
7. ### science

A rope is stretched between two boats at rest. A sailor in the first boat pulls the rope with a constant force of 100 N. First boat with the sailor has a mass of 250 kg whereas the mass of second boat is double of this mass. If

asked by Bhavya on October 2, 2015
8. ### calculus

a boat leaves a dock at 2:00 pm and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 3:00 pm. at what time were the two boats closest together

asked by LALA on November 14, 2011
9. ### Physics

Two boats are heading away from shore. Boat 1 heads due north at a speed of 3.7 m/s relative to the shore. Relative to boat 1, boat 2 is moving 35Ā° north of east at a speed of 1.3 m/s. A passenger on boat 2 walks due east across

asked by Randal on September 20, 2010
10. ### vectors

The position vectors, r km, and the velocity vectors, v km/h, of two boats at a certain time are given by ... Boat A:at 10:00 am rA=6i+10j vA=8iā2j Boat B:at 10:30 am rB=8i+5j vB=4i+j ... determine the time at which boat B

asked by Molly on February 7, 2013

More Similar Questions