A body is projected at an angle 30° with a velocity 42 `ms^(-1)` Its maximum height is

Options

A. 22.5m
B. 32.5m
C. 42.5m
D. 52.5m

Answer

To find the maximum height reached by a body projected at an angle, we can use the following steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Initial velocity \( u = 42 \, \text{m/s} \)
- Angle of projection \( \theta = 30^\circ \)
- Acceleration due to gravity \( g = 10 \, \text{m/s}^2 \) (approximated)

2. **Calculate the vertical component of the initial velocity**:
The vertical component of the initial velocity \( u_y \) can be calculated using the sine function:
\[ u_y = u \cdot \sin(\theta) = 42 \cdot \sin(30^\circ) \]
Since \( \sin(30^\circ) = \frac{1}{2} \):
\[ u_y = 42 \cdot \frac{1}{2} = 21 \, \text{m/s} \]

3. **Use the kinematic equation to find the maximum height**:
At the maximum height, the final vertical velocity \( v_y = 0 \). We can use the kinematic equation:
\[ v_y^2 = u_y^2 + 2a_y h \]
Here, \( a_y = -g \) (since gravity acts downwards), and substituting the values gives:
\[ 0 = (21)^2 + 2(-10)h \]
Rearranging this equation to solve for \( h \):
\[ 0 = 441 - 20h \]
\[ 20h = 441 \]
\[ h = \frac{441}{20} = 22.05 \, \text{m} \]

4. **Conclusion**:
The maximum height reached by the body is \( h = 22.05 \, \text{m} \).