Kicking a ball ( optimal angle)

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SUMMARY

The discussion focuses on projectile motion, specifically analyzing the trajectory of a ball kicked at a speed of 7.5 m/s at angles of 45° and 40°, landing on a flat area 5 m lower than the launch point. The calculations involve determining the time of flight, maximum height, and horizontal distance for both angles. It is established that while the optimal angle for maximum horizontal distance is 45°, the differing landing height affects the results, demonstrating that the optimal angle does not always yield the same horizontal distance when elevation changes. Additionally, the discussion explores the implications of landing on a flat area 1 m higher, prompting qualitative changes in the projectile's behavior.

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  • Familiarity with kinematic equations for motion in two dimensions
  • Knowledge of trigonometric functions for angle calculations
  • Ability to analyze changes in projectile motion due to varying initial and final 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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please i need help !
 

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