Kicking a ball ( optimal angle)

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The discussion focuses on analyzing the projectile motion of a ball kicked at speeds of 7.5 m/s at angles of 45° and 40°, landing on a flat area 5 m lower than the launch point. Participants are asked to establish a coordinate system, calculate the flight time, determine the maximum height, and compute the horizontal distance traveled for both angles. The optimal angle for maximum horizontal distance is noted as 45°, but the results for this scenario differ due to the change in vertical displacement. Additionally, the impact of changing the landing area to 1 m higher is to be examined for qualitative differences in the projectile's motion. The discussion emphasizes understanding the principles of projectile motion and the effects of varying launch angles and landing heights.
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A ball is kicked with a speed of 7.5 m/s and an angle  (relative to the horizontal) of
(a)  = 45, (b)  = 40.

The ball lands on a flat area 5 m lower than the place where it was kicked.
First describe how you choose your coordinate system (frame of reference): origin and
directions of axes used; and state the equations you apply to answer the questions below.

For both cases
(i) calculate the time the ball is flying,
(ii) determine the highest point (how high above the start),
(iii) calculate the horizontal distance it was flying
(iv) In class we found that the optimal angle for the horizontal distance is  = 45 in a
similar but di erent problem. Explain why your result here is not in contradiction to that
finding. for the problem we did it in the class y initial was equal to y final but i am not sure if this is the answer i didnt get the question !

(v) Repeat (i) { (iii) in the case when the
at area for landing is 1 m higher. What changes
qualitatively?
 
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