A stone is projected in air. Its time of flight is 3s and range is 150m. Maximum height reached by the stone is (Take, `g = 10 ms^(-2))`

Options

A. `37.5m`
B. `22.5 m`
C. `90 m`
D. `11.25m`

Explanation

To find the maximum height reached by the stone, we can follow these steps:

### Step 1: Use the Time of Flight Formula
The time of flight \( T \) for a projectile is given by the formula:
\[ T = \frac{2U \sin \theta}{g} \]
Given that the time of flight \( T = 3 \) seconds and \( g = 10 \, \text{m/s}^2 \), we can rearrange the formula to find \( U \sin \theta \):
\[ 3 = \frac{2U \sin \theta}{10} \]
Multiplying both sides by 10:
\[ 30 = 2U \sin \theta \]
Dividing both sides by 2:
\[ U \sin \theta = 15 \, \text{m/s} \]

### Step 2: Use the Maximum Height Formula
The maximum height \( H \) reached by the projectile can be calculated using the formula:
\[ H = \frac{(U \sin \theta)^2}{2g} \]
Substituting \( U \sin \theta = 15 \, \text{m/s} \) and \( g = 10 \, \text{m/s}^2 \):
\[ H = \frac{(15)^2}{2 \times 10} \]
Calculating \( (15)^2 \):
\[ H = \frac{225}{20} \]
Now, divide 225 by 20:
\[ H = 11.25 \, \text{m} \]

### Conclusion
The maximum height reached by the stone is \( 11.25 \, \text{m} \).

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