A car is traveling at a velocity of 10 km/h on a straight road. The driver of the car throws a ball. If the ball is to reach back to the driver, the direction of throw makes the following angle with the direction of the car:

Options

A. `135^@`
B. `90^@`
C. `tan ^(-1) sqrt2`
D. `tan^(-1) (1/(sqrt2))`

Explanation

To solve the problem of the car traveling at a velocity of 10 km/h and the ball being thrown by the driver such that it returns back to him, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Situation**:
- A car is moving in a straight line at a constant speed of 10 km/h.
- The driver throws a ball from the car, and we need to determine the angle at which the ball must be thrown so that it returns to the driver.

2. **Identify the Components of Motion**:
- The car has a horizontal velocity component due to its motion (10 km/h).
- When the ball is thrown, it will have both horizontal and vertical components of velocity.

3. **Determine the Horizontal Motion**:
- For the ball to return to the driver, its horizontal motion must match the motion of the car.
- If the driver throws the ball at an angle, the horizontal component of the ball's velocity must equal the speed of the car (10 km/h).

4. **Vertical Motion Consideration**:
- The vertical component of the ball's motion will determine how long it stays in the air.
- If the ball is thrown vertically upwards, it will go up and then come back down, allowing it to return to the driver.

5. **Conclusion on the Angle of Throw**:
- To ensure that the ball returns to the driver, the driver must throw the ball vertically upwards (90 degrees to the horizontal).
- This means that the angle of throw with respect to the direction of the car is 90 degrees.

### Final Answer:
The direction of throw makes an angle of **90 degrees** with the direction of the car.

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