Related questions
Question
Please solve & show steps...
![**Projectile Motion with Air Resistance - Educational Exercise**
A ball with mass 0.45 kg is thrown upward with an initial velocity of 25 m/s from the roof of a building 40 m high. Assume there is a force due to air resistance of magnitude \( \frac{v^2}{1325} \) directed opposite to the velocity, where the velocity \( v \) is measured in m/s.
**NOTE:** Use \( g = 9.8 \, \text{m/s}^2 \) as the acceleration due to gravity. Round your answers to 2 decimal places.
**Exercise**
a) Find the maximum height above the ground that the ball reaches.
**Height:** \[ \_\_\_\_\_\_\_\_\_ \text{m} \]
b) Find the time that the ball hits the ground.
**Time:** \[ \_\_\_\_\_\_\_\_\_ \text{seconds} \]
c) Use a graphing utility to plot the graphs of velocity and position versus time.
**Graph Description:**
For part (c), ensure your graphing utility is correctly set up to display two graphs:
1. **Velocity vs. Time**: This graph should show how the velocity of the ball changes over time, considering both gravity and air resistance. Expect a curve that starts at 25 m/s, decreases to zero at the peak, and then becomes negative (indicating downward motion), eventually leveling off as it approaches terminal velocity while falling.
2. **Position vs. Time**: This graph represents the ball's height above the ground over time. The curve will start at 40 m (the height of the building), rise to a maximum height (found in part a), and then decrease until it reaches zero (when the ball hits the ground).
Your plotted graphs should properly represent these relationships to give a clear visual understanding of the ball's motion under the given conditions.](https://content.bartleby.com/qna-images/question/77cac1a6-5ad9-4f72-bdd9-21a202e53df4/3ba6c0bf-c300-4915-8865-978138b79528/okcv9qq_processed.png)
Transcribed Image Text:**Projectile Motion with Air Resistance - Educational Exercise**
A ball with mass 0.45 kg is thrown upward with an initial velocity of 25 m/s from the roof of a building 40 m high. Assume there is a force due to air resistance of magnitude \( \frac{v^2}{1325} \) directed opposite to the velocity, where the velocity \( v \) is measured in m/s.
**NOTE:** Use \( g = 9.8 \, \text{m/s}^2 \) as the acceleration due to gravity. Round your answers to 2 decimal places.
**Exercise**
a) Find the maximum height above the ground that the ball reaches.
**Height:** \[ \_\_\_\_\_\_\_\_\_ \text{m} \]
b) Find the time that the ball hits the ground.
**Time:** \[ \_\_\_\_\_\_\_\_\_ \text{seconds} \]
c) Use a graphing utility to plot the graphs of velocity and position versus time.
**Graph Description:**
For part (c), ensure your graphing utility is correctly set up to display two graphs:
1. **Velocity vs. Time**: This graph should show how the velocity of the ball changes over time, considering both gravity and air resistance. Expect a curve that starts at 25 m/s, decreases to zero at the peak, and then becomes negative (indicating downward motion), eventually leveling off as it approaches terminal velocity while falling.
2. **Position vs. Time**: This graph represents the ball's height above the ground over time. The curve will start at 40 m (the height of the building), rise to a maximum height (found in part a), and then decrease until it reaches zero (when the ball hits the ground).
Your plotted graphs should properly represent these relationships to give a clear visual understanding of the ball's motion under the given conditions.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 3 steps with 4 images
Knowledge Booster
Similar questions
- You need to set up another simple ramp using the board from Part A (i.e., a board of length 1.56 mm ). (Figure 5) If the ramp must be at a 25∘∘ angle above the ground, how far back from the bed of the truck should the board touch the ground? Assume this is a different truck than the one from Part A. Express your answer in meters to three significant figures.arrow_forwardNeeds Complete solution with 100 % accuracy don't use chat gpt or ai plz plz plz. I definitely upvote you for giving me correct solution.arrow_forward
arrow_back_ios
arrow_forward_ios