Calculating Projectile Motion from a Cliff: Using Coordinates and Equations

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In summary, the conversation discusses a scenario in which a ball is kicked from the edge of a 20 m cliff with a horizontal speed of 10 m/s. The goal is to determine the initial vertical velocity, velocity and speed before the ball hits the ground, angle at which it was kicked, horizontal distance between the cliff and landing point, and the total distance traveled. To solve these questions, a coordinate system is established with an origin and directions for the axes. The equations used to answer the questions include the Pythagorean Theorem to find the distance between the starting and landing point.
  • #1
mahrouqi
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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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  • #2
Since they are seeking the distance from point A to point B, I would use Pythagorean Theorem.
 
  • #3
thanks for ur answer
 

What is the initial velocity of the ball?

The initial velocity of the ball will depend on a variety of factors such as the force of the kick, the angle at which the ball is kicked, and the air resistance. Without specific data, it is difficult to determine the exact initial velocity.

What is the trajectory of the ball?

The trajectory of the ball will also depend on several factors. The angle of the kick, the initial velocity, and the air resistance will all affect the path of the ball. In general, the ball will follow a parabolic path until it reaches the ground.

What is the impact force of the ball when it hits the ground?

The impact force of the ball will depend on the mass of the ball and the velocity at which it hits the ground. The higher the velocity, the greater the impact force will be. This is why it is important to consider safety precautions when kicking a ball from a cliff.

How long will it take for the ball to reach the ground?

The time it takes for the ball to reach the ground will depend on the initial velocity and the height of the cliff. Using the formula t=sqrt(2h/g), where t is time, h is height, and g is the acceleration due to gravity, we can estimate the time it will take for the ball to reach the ground.

What will happen to the ball when it reaches the ground?

When the ball reaches the ground, it will experience an impact force and bounce back up. The height it bounces will depend on the elasticity of the ball and the surface it lands on. It may also roll or bounce in different directions depending on the angle at which it hits the ground.

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