A ball with mass 0.45 kg is thrown upward with initial velocity 25 m/s from the roof of a building 40 m high. Assume there is a force due to v2 directed opposite to the velocity, 1325 air resistance of magnitude where the velocity v is measured in m/s. NOTE: Use g=9.8 m/s² as the acceleration due to gravity. Round your answers to 2 decimal places. a) Find the maximum height above the ground that the ball reaches. Height: m b) Find the time that the ball hits the ground. Time: seconds
A ball with mass 0.45 kg is thrown upward with initial velocity 25 m/s from the roof of a building 40 m high. Assume there is a force due to v2 directed opposite to the velocity, 1325 air resistance of magnitude where the velocity v is measured in m/s. NOTE: Use g=9.8 m/s² as the acceleration due to gravity. Round your answers to 2 decimal places. a) Find the maximum height above the ground that the ball reaches. Height: m b) Find the time that the ball hits the ground. Time: seconds
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![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77cac1a6-5ad9-4f72-bdd9-21a202e53df4%2F3ba6c0bf-c300-4915-8865-978138b79528%2Fokcv9qq_processed.png&w=3840&q=75)
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.
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