2. On top of a tower (30 m from the ground), an object is launched straight up with an initial velocity vo. The object continues its flight in free fall to a maximum height of 65 meter from top of the tower. After reaching the maximum height, the object falls back to the ground. a. What is initial velocity vo of the object (at the height of 30 m) b. What is the velocity of the object just before it hits the ground? c. What is the total duration of the object's flight? d. Draw a position-time, velocity-time, and acceleration-time graph to show the motion of the object

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On top of a tower (30 m from the ground), an object is launched
straight up with an initial velocity ?0. The object continues its flight in free fall to a maximum height of 65 meter from top of the tower. After reaching the maximum height, the object falls back to the ground.

### Physics Problem: Projectile Motion

**Scenario:**
On top of a tower (30 m from the ground), an object is launched straight up with an initial velocity \( v_0 \). The object continues its flight in free fall to a maximum height of 65 meters from the top of the tower. After reaching the maximum height, the object falls back to the ground.

**Questions:**

a. What is the initial velocity \( v_0 \) of the object (at the height of 30 m)?

b. What is the velocity of the object just before it hits the ground?

c. What is the total duration of the object’s flight?

d. Draw a position-time, velocity-time, and acceleration-time graph to show the motion of the object.

**Graph Explanation:**

For part d, to visualize the motion, create three separate graphs:

1. **Position-Time Graph:** 
   - This graph shows the position of the object over time. 
   - Start at 30 m (height of the tower). 
   - The curve initially rises to the peak height (65 m above the tower), then descends back to the ground (0 m).

2. **Velocity-Time Graph:** 
   - This graph shows the velocity of the object as time passes. 
   - It begins with the initial velocity \( v_0 \), decreases to 0 at the peak height, and then increases negatively (downward) as the object falls.

3. **Acceleration-Time Graph:** 
   - This graph illustrates constant acceleration due to gravity.
   - The line will be horizontal, representing constant negative acceleration (approximately -9.81 m/s²). 

These graphs help in understanding the dynamics of projectile motion, highlighting changes in position, velocity, and acceleration over time.
Transcribed Image Text:### Physics Problem: Projectile Motion **Scenario:** On top of a tower (30 m from the ground), an object is launched straight up with an initial velocity \( v_0 \). The object continues its flight in free fall to a maximum height of 65 meters from the top of the tower. After reaching the maximum height, the object falls back to the ground. **Questions:** a. What is the initial velocity \( v_0 \) of the object (at the height of 30 m)? b. What is the velocity of the object just before it hits the ground? c. What is the total duration of the object’s flight? d. Draw a position-time, velocity-time, and acceleration-time graph to show the motion of the object. **Graph Explanation:** For part d, to visualize the motion, create three separate graphs: 1. **Position-Time Graph:** - This graph shows the position of the object over time. - Start at 30 m (height of the tower). - The curve initially rises to the peak height (65 m above the tower), then descends back to the ground (0 m). 2. **Velocity-Time Graph:** - This graph shows the velocity of the object as time passes. - It begins with the initial velocity \( v_0 \), decreases to 0 at the peak height, and then increases negatively (downward) as the object falls. 3. **Acceleration-Time Graph:** - This graph illustrates constant acceleration due to gravity. - The line will be horizontal, representing constant negative acceleration (approximately -9.81 m/s²). These graphs help in understanding the dynamics of projectile motion, highlighting changes in position, velocity, and acceleration over time.
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