Solving a Ball Thrown from a Cliff: Angle and Distance

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SUMMARY

The discussion focuses on projectile motion problems involving a cannon and a thrown rock. A cannon, positioned 60 meters from a 25-meter high cliff, requires a minimum muzzle velocity to clear the cliff when fired at a 43-degree angle. Additionally, a rock thrown from a 15-meter tall building at 30 m/s and 33 degrees is analyzed for its maximum height and impact distance. Lastly, a scenario involving a ball thrown from a 45-meter cliff is examined to determine the angle needed for a runner to catch it before it hits the ground.

PREREQUISITES
  • Understanding of projectile motion principles
  • Knowledge of trigonometric functions for angle calculations
  • Familiarity with kinematic equations
  • Basic physics concepts related to velocity and acceleration
NEXT STEPS
  • Calculate the minimum muzzle velocity for projectiles using kinematic equations
  • Explore the effects of launch angle on projectile range and height
  • Learn about the trajectory of projectiles in varying gravitational fields
  • Investigate real-world applications of projectile motion in sports and engineering
USEFUL FOR

Students studying physics, educators teaching projectile motion, and engineers involved in trajectory analysis will benefit from this discussion.

yojayydee
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A cannon located 60m from the base of a vertical 25 m cliff shoots a shell at 43 degrees above the horizontal.

What is the minimum muzzle velocity be for the shell to clear the top of the cliff ?
The ground at the top of the cliff is level, with constant elevation of 25 m above the cannon, How far does the shell land past the cliff ?
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A man stands on the roof of a 15 m tall building a throws a rock with a velocity of magnitude 30 m/s at an angle of 33 degrees above the horizontal.

What is the maximum height above the roof reached by the rock .?
The magnitude of the velocity of the rock before it strikes the ground ?
The horizontal distance from the base of the building to the point when the rock strikes the ground .?
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A ball is thrown upward with an initial spped of 20 m/s from the edge of a 45 m high cliff. At the istant the ball is thrown, a woman starts running away from the base of the cliff with a constant speed of 6 m/s .
At what angle above the horizontal should the ball be thrown so the runner will catch it just before it hits the ground and how far does the women wrun before she catches the ball .?
 
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yojayydee said:
A cannon located 60m from the base of a vertical 25 m cliff shoots a shell at 43 degrees above the horizontal.

What is the minimum muzzle velocity be for the shell to clear the top of the cliff ?
The ground at the top of the cliff is level, with constant elevation of 25 m above the cannon, How far does the shell land past the cliff ?

Hi yojayydee! :smile:

Show us what you've tried, and where you're stuck, and then we'll know how to help. :smile:
 

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