A boy standing on a long railroad car throuws a ball straight upwards. The car is moving on the horizontal road with an acceleration of `1m/s^2` and the projectioon velocity inte vertical direction is 9.8 m/s. How far behind the boy will the ball fall on the car?

Explanation

To solve the problem, we need to determine how far behind the boy the ball will fall on the moving railroad car after being thrown straight upwards. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Motion of the Ball
The ball is thrown straight up with an initial vertical velocity of \(9.8 \, \text{m/s}\). The only force acting on the ball after it is thrown is gravity, which will decelerate it at a rate of \(9.8 \, \text{m/s}^2\).

### Step 2: Calculate the Time of Flight
The time of flight \(t\) can be calculated using the formula for the time taken to reach the maximum height and then return to the original height:
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