Projectile Motion and Free Fall Calculation Challenge

Question:

A ball is thrown with an initial horizontal velocity of 6 m/s off of a rooftop. If the ball lands 1.6 seconds later, what is the height of the roof? How far away from the house did the ball land?

Answer:

Final answer: The height of the roof from which the ball was thrown is approximately 12.54 meters, and the ball landed 9.6 meters away from the house.

Explanation:

The question posed is about projectile motion, which is a calculus form of linear motion. Here, the acceleration acting on the thrown ball is due to gravity, which in this context is 9.8 m/s².

To determine the height of the roof, we use the equation of motion: height = 1/2gt^2, substituting the known values, we get; height = 1/2*9.8*(1.6)^2 = approx 12.54 meters. So the option that matches these calculations isn't provided in the multiple choices, perhaps a typing error occurred in the question.

For the horizontal distance covered by the ball, we use the formula: distance = speed*time. Substituting the known values, we get; distance = 6*1.6 = 9.6 meters. From this, the ball landed 9.6 meters away from the house.