A toy rocket is launched with an initial velocity of 10.0 m/s in the horizontal direction from the roof of a 30.0 m -tall building. The rocket's engine produces a horizontal acceleration of (1.60 m/s3)t, in the same direction as the initial velocity, but in the vertical direction the acceleration is g , downward. Air resistance can be neglected. What horizontal distance does the rocket travel before reaching the ground?

The toy rocket will do an horizontal distance of 27.793 meters before reaching the ground.

Explanation:

This rocket experiments a two-dimension motion consisting in a combination of vertical free-fall and a horizontal uniformly acclerated motion. Flight time is governed by vertical movement and can be found by using this formula:

Where:

- Initial height, measured in meters.

- Initial vertical speed, measured in meters per second.

- Time, measured in seconds.

- Gravitational acceleration, measured in meters per square second.

- Current height, measured in meters.

If we know that , , and , then resulting polynomial is solved:

The time taken by the toy rocket is:

Now, the horizontal distance can be found by integrating acceleration function twice. That is:

If we know that and , then the horizontal position formula is:

Where:

- Horizontal position, measured in meters.

- Time, measured in seconds.

Now, the horizontal distance before reaching the ground is found: ()

The toy rocket will do an horizontal distance of 27.793 meters before reaching the ground.

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