Question

a rocket is being launched. after a while, it rises at a constant velocity of 30 miles per second. an observer is standing 112 miles from the launching site. how fast is the distance between the rocket and the observer changing when the rocket is at a height of 15 miles? present your answer as an approximation, accurate up to three or more decimals.

Answer 1

To find the rate at which the distance between the rocket and the observer is changing, we can use the concept of related rates. Using the Pythagorean theorem and differentiating with respect to time, we can find the desired rate.

Step-by-step explanation:

To find the rate at which the distance between the rocket and the observer is changing, we can use the concept of related rates. Let's denote the distance between the rocket and the observer as 'd' and the height of the rocket as 'h'. We are given that the rocket rises at a constant velocity of 30 miles per second.

Using the Pythagorean theorem, we can write: d^2 = h^2 + 112^2

Differentiating both sides of the equation with respect to time, we get: 2d*(dd/dt) = 2h*(dh/dt)

Since we are interested in finding the rate at which 'd' is changing when 'h' is 15 miles, we can substitute the given values into the equation and solve.

Answer 2

The rate of change of distance between the rocket and the observer is 30 miles per second.

Step-by-step explanation:

To find how fast the distance between the rocket and the observer is changing, we can use the concept of velocity. The velocity of the rocket is given as 30 miles per second. We can consider the observer's distance from the launching site as the displacement. Using the formula velocity = displacement / time, we can rearrange the formula to calculate the rate of change of the distance:

Rate of change of distance = velocity

So, the rate of change of distance between the rocket and the observer is 30 miles per second.