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Solution: A cannon, located 60.0 m from the base of a
Chapter 3, Problem 55P(choose chapter or problem)
Problem 54P
A cannon, located 60.0 m from the base of a vertical 25.0-m-tall cliff, shoots a 15-kg shell at 43.0o above the horizontal toward the cliff. (a) What must the minimum muzzle velocity be for the shell to clear the top of the cliff? (b) The ground at the top of the cliff is level, with a constant elevation of 25.0 m above the cannon. Under the conditions of part (a), how far does the shell land past the edge of the cliff?
Questions & Answers
QUESTION:
Problem 54P
A cannon, located 60.0 m from the base of a vertical 25.0-m-tall cliff, shoots a 15-kg shell at 43.0o above the horizontal toward the cliff. (a) What must the minimum muzzle velocity be for the shell to clear the top of the cliff? (b) The ground at the top of the cliff is level, with a constant elevation of 25.0 m above the cannon. Under the conditions of part (a), how far does the shell land past the edge of the cliff?
ANSWER:
Solution 54P
Step 1
(a) Let us consider the muzzle velocity is .
Hence the x component of the velocity is
And y component of the velocity is
Now the cliff is located at 60 m away from the initial position of the projectile. So the time taken by the projectile to reach the cliff is
Now the vertical position of the projectile in this time will be
Now this height must be 25 m to just clear the cliff, hence we must have
Hence the muzzle velocity should be 32.7 m/s to just clear the cliff.