An object is projected upwards with a velocity of `100m//s`. It will strike the ground after (approximately)

Options

A. 10sec
B. 20sec
C. 15sec
D. 5sec

Answer

To solve the problem of an object projected upwards with an initial velocity of \(100 \, \text{m/s}\), we need to determine how long it will take for the object to strike the ground after being thrown.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial velocity (\(u\)) = \(100 \, \text{m/s}\) (upwards)
- Acceleration due to gravity (\(a\)) = \(-10 \, \text{m/s}^2\) (acting downwards)
- Displacement (\(\Delta x\)) = \(0\) (the object returns to the original launch height)

2. **Use the Kinematic Equation:**
The kinematic equation we will use is:
\[ \Delta x = u t + \frac{1}{2} a t^2 \]
Substituting the known values:
\[ 0 = 100t + \frac{1}{2}(-10)t^2 \]

3. **Simplify the Equation:**
This simplifies to:
\[ 0 = 100t - 5t^2 \]
Rearranging gives:
\[ 5t^2 - 100t = 0 \]

4. **Factor the Equation:**
Factoring out \(t\):
\[ t(5t - 100) = 0 \]

5. **Solve for \(t\):**
This gives us two solutions:
\[ t = 0 \quad \text{or} \quad 5t - 100 = 0 \]
Solving \(5t - 100 = 0\):
\[ 5t = 100 \quad \Rightarrow \quad t = 20 \, \text{seconds} \]

6. **Conclusion:**
The object will strike the ground after approximately \(20\) seconds.