Ch1 Ex 1B Q7 A balloon at a height of 300 m is descending at 10 ms-1 …

The Problem:

A balloon at a height of 300 m is descending at 10 ms-1 and decelerating at a rate of 0.4 ms-2 How long will it take for the balloon to stop descending, and what will its height be then?

The Problem:

A balloon at a height of 300 m is descending at 10 ms-1 and decelerating at a rate of 0.4 ms-2 How long will it take for the balloon to stop descending, and what will its height be then?

Douglas Quadling Mechanics 1
Exercise 1B Q7

A balloon at a height of 300 m is descending at 10 ms and decelerating at a rate of 0.4 ms 2….

3 October 2023 by alevelmechanics1

Problem Statement

A balloon at a height of 300 m is descending at 10 m/s and decelerating at a rate of 0.4 m/s². How long will it take for the balloon to stop descending, and what will its height be then?

Solution

Given:

• Initial height (h₀) = 300 m
• Initial velocity (u) = 10 m/s (descending)
• Deceleration (a) = -0.4 m/s² (opposes motion)
• Final velocity (v) = 0 m/s (balloon stops descending)

Step 1: Find the Time (t) for the Balloon to Stop Descending

We use the equation of motion:

v = u + a * t

Substitute the values:

0 = 10 + (-0.4) * t
0 = 10 - 0.4t
0.4t = 10
t = 10 / 0.4
t = 25 seconds

Time for the balloon to stop descending = 25 seconds

Step 2: Calculate the Height (h) When the Balloon Stops

We use the equation of motion:

s = u * t + 0.5 * a * t²

Substitute the values:

s = 10 * 25 + 0.5 * (-0.4) * (25)²
s = 250 + 0.5 * (-0.4) * 625
s = 250 - 0.2 * 625
s = 250 - 125
s = 125 m

The balloon descends 125 meters before stopping. Therefore, its final height is:

h = h₀ - s
h = 300 - 125
h = 175 m

Final height of the balloon = 175 meters

Final Answers:

1. Time for the balloon to stop descending = 25 seconds
2. Final height of the balloon = 175 meters