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Calculate Range, Final Speed and Direction of a Projectile Shot Horizontally off a Cliff
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Apply the kinematic equations in both the horizontal and vertical axis to find the horizontal range as well as the final speed of a ball which is shot horizontally off a 30m high cliff with an initial velocity of 20m/s.
By breaking the motion up into horizontal and vertical components we can look at the motion of the ball as at travels in projectile motion from the top of the cliff to the bottom. By the time the ball lands on the ground it will have some vertical and horizontal displacement which we will solve for. Then using the components of the final velocity we will use the Pythagorean theorem along with an inverse tangent in order to solve for the final speed and direction of the ball.
The key in the solution to this problem is that the projectile is only accelerating downward due to gravity, there is no acceleration in the vertical axis. Additionally the only quantity coupling the two axes of motion together is time, which is always the same for both the x and y motion of the projectile.
This problem commonly comes up when learning about projectile motion in introductory physics courses such as high school physics, AP Physics 1, AP Physics C Mechanics and appears on the JEE.
By breaking the motion up into horizontal and vertical components we can look at the motion of the ball as at travels in projectile motion from the top of the cliff to the bottom. By the time the ball lands on the ground it will have some vertical and horizontal displacement which we will solve for. Then using the components of the final velocity we will use the Pythagorean theorem along with an inverse tangent in order to solve for the final speed and direction of the ball.
The key in the solution to this problem is that the projectile is only accelerating downward due to gravity, there is no acceleration in the vertical axis. Additionally the only quantity coupling the two axes of motion together is time, which is always the same for both the x and y motion of the projectile.
This problem commonly comes up when learning about projectile motion in introductory physics courses such as high school physics, AP Physics 1, AP Physics C Mechanics and appears on the JEE.
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