On plant Teher, the free-fall acceleration is the same as that on Earth but there is also a strong downward electric field that is unyorm close to the planet's Surface: A 2.ooks Sall having a charge of Charge of 6.00 Mc is thrown upward it a speed of 22.0 m/s. and it hits the ground fter an interval of 4.505. What is the poten- ial difference between the starting point and The top pint of the trajectory 2

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**Physics Problem: Understanding Free-Fall and Electric Fields on Planet Tehar**

**Problem Statement:**

On planet Tehar, the free-fall acceleration is the same as that on Earth, but there is also a strong downward electric field that is uniform close to the planet's surface. A 2.00 kg ball having a charge of 6.00 μC is thrown upward at a speed of 20.0 m/s and it hits the ground after an interval of 4.50 s. What is the potential difference between the starting point and the top point of the trajectory?

**Analysis and Solution:**

1. **Free-Fall Acceleration (g):**
   - Since the free-fall acceleration on planet Tehar is the same as on Earth, we use \( g = 9.8 \, \text{m/s}^2 \).

2. **Initial Information:**
   - Mass of ball, \( m = 2.00 \, \text{kg} \)
   - Charge of the ball, \( q = 6.00 \, \mu\text{C} = 6.00 \times 10^{-6} \, \text{C} \)
   - Initial speed, \( v_0 = 20.0 \, \text{m/s} \)
   - Total time of flight, \( t = 4.50 \, \text{s} \)

3. **Trajectory and Time Calculation:**
   - The ball is thrown upward and returns to the ground, hence the total time for ascending and descending is 4.50 s.
   - Time to reach the top of the trajectory, \( t_{\text{up}} = \frac{4.50 \, \text{s}}{2} = 2.25 \, \text{s} \)

4. **Vertical Displacement Calculation:**
   - Using the kinematic equation \( v = u + at \):
     \[
     0 = 20.0 \, \text{m/s} - (9.8 \, \text{m/s}^2) \times 2.25 \, \text{s}
     \]
     This confirms the time to the top point as accurate since \( v = 0 \, \text{m/s} \) at the top.

5. **Height Calculation (h):**
   - Using \( h
Transcribed Image Text:**Physics Problem: Understanding Free-Fall and Electric Fields on Planet Tehar** **Problem Statement:** On planet Tehar, the free-fall acceleration is the same as that on Earth, but there is also a strong downward electric field that is uniform close to the planet's surface. A 2.00 kg ball having a charge of 6.00 μC is thrown upward at a speed of 20.0 m/s and it hits the ground after an interval of 4.50 s. What is the potential difference between the starting point and the top point of the trajectory? **Analysis and Solution:** 1. **Free-Fall Acceleration (g):** - Since the free-fall acceleration on planet Tehar is the same as on Earth, we use \( g = 9.8 \, \text{m/s}^2 \). 2. **Initial Information:** - Mass of ball, \( m = 2.00 \, \text{kg} \) - Charge of the ball, \( q = 6.00 \, \mu\text{C} = 6.00 \times 10^{-6} \, \text{C} \) - Initial speed, \( v_0 = 20.0 \, \text{m/s} \) - Total time of flight, \( t = 4.50 \, \text{s} \) 3. **Trajectory and Time Calculation:** - The ball is thrown upward and returns to the ground, hence the total time for ascending and descending is 4.50 s. - Time to reach the top of the trajectory, \( t_{\text{up}} = \frac{4.50 \, \text{s}}{2} = 2.25 \, \text{s} \) 4. **Vertical Displacement Calculation:** - Using the kinematic equation \( v = u + at \): \[ 0 = 20.0 \, \text{m/s} - (9.8 \, \text{m/s}^2) \times 2.25 \, \text{s} \] This confirms the time to the top point as accurate since \( v = 0 \, \text{m/s} \) at the top. 5. **Height Calculation (h):** - Using \( h
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