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A model rocket is launched from the ground. If it takes 13.6 seconds for the rocket to crash into the ground 240 meters from the launch site, what was the initial speed of the rocket? Assume the rocket is in free fall while in the air.

Answer :

Final answer:

The initial speed of the rocket, based on the given range and time of flight, is approximately 17.65 m/s.

Explanation:

The question is asking for the initial speed of a model rocket that is launched and then crashes back onto the ground after a certain amount of time and distance. Essentially, we are looking at a case of projectile motion, which encompasses both horizontal motion and vertical motion.

The time for the rocket's flight is completely determined by the vertical motion. However, the information given doesn't involve heights, it involves the horizontal distance covered i.e., range (240m) of the projectile and the time of flight (13.6s). Therefore, we should focus on the horizontal aspects of the motion to find the initial speed of the rocket.

For horizontal motion in projectile motion, we can use the formula: Range = (Initial speed) * (Time of flight), since horizontal motion is a constant velocity in the absence of air resistance. By re-arranging this formula, we can find the initial speed: Initial speed = Range / Time of flight. So, the initial speed of the rocket would be 240m / 13.6s, which approximates to 17.65 m/s.

Learn more about Projectile Motion here:

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