A plane flying horizontally at `100 m s^-1` releases an object which reaches the ground in `10 s`. At what angle with horizontal it hits the ground ?

Options

A. `55^@`
B. `45^@`
C. `60^@`
D. `75^@`

Explanation

To solve the problem, we need to determine the angle at which the object hits the ground after being released from a plane flying horizontally at a speed of 100 m/s. The object takes 10 seconds to reach the ground.

### Step-by-Step Solution:

1. **Identify the Components of Motion**:
- The motion of the object can be broken down into horizontal (x-direction) and vertical (y-direction) components.
- The horizontal velocity (Vx) is constant at 100 m/s (the speed of the plane).
- The vertical motion is influenced by gravity.

2. **Calculate the Vertical Velocity (Vy)**:
- The object falls under the influence of gravity, which accelerates it downwards at approximately \( g = 9.8 \, \text{m/s}^2 \).
- The vertical velocity at the time of impact can be calculated using the formula:
\[ Vy = g \cdot t \]
- Substituting the values:
\[ Vy = 9.8 \, \text{m/s}^2 \cdot 10 \, \text{s} = 98 \, \text{m/s} \]

3. **Determine the Resultant Velocity (V)**:
- The resultant velocity (V) just before impact can be found using the Pythagorean theorem since the horizontal and vertical components are perpendicular:
\[ V = \sqrt{Vx^2 + Vy^2} \]
- Substituting the values:
\[ V = \sqrt{(100 \, \text{m/s})^2 + (98 \, \text{m/s})^2} \]
\[ V = \sqrt{10000 + 9604} = \sqrt{19604} \approx 140 \, \text{m/s} \]

4. **Calculate the Angle of Impact (θ)**:
- The angle θ with respect to the horizontal can be found using the tangent function:
\[ \tan(\theta) = \frac{Vy}{Vx} \]
- Substituting the values:
\[ \tan(\theta) = \frac{98}{100} \]
\[ \theta = \tan^{-1}(0.98) \]
- Calculating θ:
\[ \theta \approx 44.6^\circ \]

5. **Final Result**:
- The angle at which the object hits the ground is approximately \( 44.6^\circ \) with respect to the horizontal.

### Summary:
The object released from the plane hits the ground at an angle of approximately \( 44.6^\circ \) with respect to the horizontal.