Calculating Projectile Motion from a Cliff: Using Coordinates and Equations

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To analyze the projectile motion of a ball kicked from a 20 m cliff with a horizontal speed of 10 m/s, a coordinate system is established with the origin at the cliff's edge, the x-axis directed horizontally, and the y-axis directed vertically downward. The initial vertical velocity must be calculated to ensure the ball lands after 3 seconds, leading to the determination of the vertical velocity and final speed before impact. The angle of projection relative to the horizontal can be derived from the initial velocities, and the horizontal distance traveled can be calculated using the time of flight. For the distance between the starting point and the landing point, the Pythagorean theorem is suggested as the appropriate method to find the resultant distance. The discussion emphasizes the importance of understanding the equations of motion in solving projectile problems effectively.
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From the edge of a cli of height 20 m a (heavy) ball is kicked. Neglect air resistance. The
horizontal speed is 10 m/s (directed away from the cli ). The vertical velocity is chosen
such that the ball lands on the ground below the cliff after
3 s.

First describe how you choose your coordinate system (frame of reference): origin and di-
rections of axes used; and state the equations you apply to answer the questions below.

determine
(i) the initial vertical velocity,
(ii) the velocity and the speed of the ball just before it hits the ground,
(iii) the angle  (relative to the horizontal) when it was kicked o ,
(iv) the horizontal distance between the cli and the point where the ball landed,
(v) the distance between the starting point on top of the cli and the landing point.


I solved the questions from i-iv , but i need help how can I do the v question is it by using Pythagoras theorem ? or ?


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The Attempt at a Solution

 
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Since they are seeking the distance from point A to point B, I would use Pythagorean Theorem.
 
thanks for ur answer
 
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