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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

Distance Two boats leave the same port at the same time, with boat A traveling north at 15 knots (nautical miles per hour) and boat B traveling east at 20 knots. How fast is the distance between them changing when boat A is 30 nautical miles from port?

To determine

To calculate: How fast is the distance between the boats changing when boat A is 30 nautical miles from port and boat A is travelling north at 15 knots and boat B is travelling east at 20 knots.

Explanation

Given Information:

Boat A is 30 nautical miles from port and boat A is travelling north at 15 knots and boat B is travelling east at 20 knots.

Formula used:

According to the Pythagoras theorem,

a2+b2=c2

Where a,b,c are the sides of the triangle.

According to the chain rule differentiation, if y=f(u), where u=g(x), then y is a differentiable function of x.

dydx=dydududx

The derivative of a constant value, k, is

ddx(k)=0

According to the sum rule of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

f(x)=u(x)+v(x)

Calculation:

As it is provided that boat A is 30 nautical miles from port and boat A is travelling north at 15 knots and boat B is travelling east at 20 knots.

Thus, this arrangement can be considered as a right angled triangle with the distance between the boats as hypotenuse and the distance of boat A from the port be the altitude and distance of boat B from the port be the base of the triangle.

Now, let A be the distance of boat A from the port, B be the distance of boat B from the port and x be the distance between both the ports then, according to the Pythagoras theorem,

So,

x2=A2+B2 …… (1)

Differentiate the equation (1) with respect to t by the use of sum rule and chain rule of derivative as,

2xdxdt=2AdAdt+2BdBdt …… (2)

Now, the rate at which the distance between the boats is changing when A is 30 nautical miles from the port is to be obtained

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Chapter 11 Solutions

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