A truck is moving with a constant velocity of `54 km h^-1`. In which direction (angle with the direction of motion of truck) should a stone be projected up with a velocity of `20 ms^-1`, from the floor of the truck of the truck, so as to appear at right angles to the truck, for a person standing on earth ?

Options

A. `cos^-1 (-(3)/(4))`
B. `cos^-1 (-(1)/(4))`
C. `cos^-1 (-(2)/(4))`
D. `cos^-1 ((3)/(4))`

Explanation

To solve the problem, we need to determine the angle at which a stone should be projected from a moving truck so that it appears to move at right angles to the truck for an observer on the ground.

### Step-by-Step Solution:

1. **Convert the truck's velocity from km/h to m/s**:
\[ \text{Velocity of truck} (V_T) = 54 \text{ km/h} = \frac{54 \times 1000}{3600} = 15 \text{ m/s} \]

2. **Identify the stone's projection velocity**:
\[ \text{Velocity of stone with respect to truck} (V_B) = 20 \text{ m/s} \]

3. **Set up the relative motion equation**:
The velocity of the stone with respect to the ground can be expressed as:
\[ V_{B,G} = V_B \cdot \cos(\theta) + V_T \quad \text{(horizontal component)} \]
\[ V_{B,G} = V_B \cdot \sin(\theta) \quad \text{(vertical component)} \]
Here, \( V_{B,G} \) is the velocity of the stone with respect to the ground.

4. **Condition for right angles**:
For the stone to appear at right angles to the truck, the horizontal component of the stone's velocity must be zero when viewed from the ground:
\[ V_B \cdot \cos(\theta) = V_T \]

5. **Substituting the known values**:
\[ 20 \cdot \cos(\theta) = 15 \]
\[ \cos(\theta) = \frac{15}{20} = \frac{3}{4} \]

6. **Finding the angle**:
To find the angle \( \theta \):
\[ \theta = \cos^{-1}\left(\frac{3}{4}\right) \]

7. **Calculating the angle**:
Using a calculator:
\[ \theta \approx 41.41^\circ \]

### Final Answer:
The stone should be projected at an angle of approximately \( 41.41^\circ \) with respect to the vertical (upward direction) from the floor of the truck.