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Chapter 2: Problem 59

In the problems, please assume the free-fall acceleration $g=9.80 \mathrm{m} / \mathrm{s}^{2}$ unless a more precise value is given in the problem statement. Ignore air resistance. A rocket is launched from rest. After 8.0 min, it is \(160 \mathrm{km}\) above the Earth's surface and is moving at a speed of $7.6 \mathrm{km} / \mathrm{s} .$ Assuming the rocket moves up in a straight line, what are its (a) average velocity and (b) average acceleration?

Short Answer

Expert verified
Answer: The rocket's average velocity is 333.33 m/s, and its average acceleration is 15.83 m/s² during the first 8 minutes of flight.

Step by step solution

01

Convert units to SI system

Before starting our calculations, it's important to convert all the values to SI units. Convert 160 km to meters and 7.6 km/s to meters per second: 160 km = 160,000 meters 7.6 km/s = 7,600 meters per second
02

Find the time interval in seconds

We are given the time interval of 8.0 minutes. Let's convert this to seconds: 8.0 minutes * 60 seconds/minute = 480 seconds
03

(a) Calculate the average velocity

Average velocity is given by the formula: \(Average\_velocity = \frac{Final\_position - Initial\_position}{Time\_interval}\) Since the rocket is launched from rest and moves up in a straight line: Initial position = 0 Final position = 160,000 meters Time interval = 480 seconds The average velocity can be calculated as follows: \(Average\_velocity = \frac{160,000 - 0}{480} = \frac{160,000}{480} = 333.33 \mathrm{m/s}\)
04

(b) Calculate the average acceleration

Average acceleration is given by the formula: \(Average\_acceleration = \frac{Final\_velocity - Initial\_velocity}{Time\_interval}\) Since the rocket is launched from rest: Initial velocity = 0 Final velocity = 7,600 meters per second Time interval = 480 seconds The average acceleration can be calculated as follows: \(Average\_acceleration = \frac{7,600 - 0}{480} = \frac{7,600}{480} = 15.83 \mathrm{m/s^2}\) In conclusion, the rocket's (a) average velocity is 333.33 m/s and (b) average acceleration is 15.83 m/s².

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