An object is thrown upward with a vertical velocity of 128 ft./sec. It will return in

Options

A. 64 seconds
B. 16 seconds
C. 8 seconds
D. 4 seconds

Explanation

To solve the problem of how long it takes for an object thrown upward at a velocity of 128 ft/sec to return to the ground, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Initial velocity (u) = 128 ft/sec
- Final velocity (v) at the highest point = 0 ft/sec
- Acceleration (a) due to gravity = -32 ft/sec² (since gravity acts downward)

2. **Use the Equation of Motion**:
We can use the first equation of motion:
\[ v = u + at \]
At the highest point, the final velocity (v) is 0. Therefore, we can rearrange the equation to solve for time (t):
\[ 0 = 128 - 32t \]

3. **Solve for Time (t)**:
Rearranging the equation gives:
\[ 32t = 128 \]
\[ t = \frac{128}{32} = 4 \text{ seconds} \]

4. **Calculate Total Time for the Object to Return**:
The time taken to go up is the same as the time taken to come down. Therefore, the total time (T) for the object to return to the ground is:
\[ T = 2t = 2 \times 4 = 8 \text{ seconds} \]

5. **Final Answer**:
The object will return in **8 seconds**.