To show that the increase in surface area of a homemade rocket decreases the time of flight when launched at 90 degrees, we need to consider the effect of air resistance on the rocket's motion.
When a rocket is launched, it experiences air resistance due to its interaction with the surrounding air. Air resistance opposes the motion of the rocket and can significantly affect its flight dynamics. The surface area of the rocket plays a crucial role in determining the amount of air resistance it experiences.
Typically, rockets have a streamlined shape with a smaller cross-sectional area in the direction of motion to minimize air resistance. However, if the surface area of the rocket is increased, it will result in a larger drag force acting on the rocket.
When a rocket is launched vertically (at 90 degrees), the force of gravity acts to pull it down, while the drag force acts in the opposite direction. The net force on the rocket determines its acceleration, and hence its time of flight.
If the surface area of the rocket is increased, the drag force will also increase. As a result, the net force acting on the rocket will decrease, leading to a reduced acceleration. Since the rocket spends less time accelerating, its time of flight will be shorter.
In summary, increasing the surface area of a homemade rocket launched at 90 degrees increases the drag force acting on the rocket, reducing the net force and acceleration. This decrease in acceleration results in a shorter time of flight for the rocket.