Question

During the first 40 s of a rocket flight, the rocket is propelled straight up so that in t seconds it reaches a height of

s=0.3t 3ft. What is the average velocity of the rocket during the first 1000 ft of its flight?

Answer 1

To find the average velocity of the rocket during its ascent to 1000 ft, we solve the cubic equation s=0.3t^3 for t when s equals 1000 ft, then calculate the average velocity by dividing the distance (1000 ft) by this time.

Step-by-step explanation:

The student is asking how to calculate the average velocity of a rocket during the first 1000 ft of its flight, given that the rocket's height in feet after t seconds is described by the equation s=0.3t^3. To find the average velocity, we need to determine the time it takes for the rocket to reach 1000 feet and then divide the distance by this time.

1. First, we set the height equation s=0.3t^3 equal to 1000 ft to find the time at which the rocket reaches this height: 1000 = 0.3t^3.
2. Solving for t gives us the cube root of (1000/0.3), which equals t.
3. We then take the total distance traveled, which is 1000 ft, and divide it by the time to get the average velocity.