A pirate ship is rapidly approaching your fort! You bravely station yourself at the mounted cannon but find to your dismay that you have only one cannonball. Not only this, yoour cannon is rusted in place and can only fire at an angle theta = 10.0 degrees up from the horizontal. To prevent a siege on your fort, you must fire your cannon at exactly the correct moment to strike the enemy ship at the base of its mast. You know that your cannon is stationed on a wall a height h = 8.00 m above your target , and that it fires at a speed of v1 = 205 m/s. You will use this information to determine the distance d at which the pirate ship is in your cannon's range. Part 1: Determine the initial vertical velocity v1,y and the initial horizonal velocity v1,x of the cannonball. Part 2: If the cannonball starts its trajectory at a height y1 = h, determine its height y2 at the top of its arc and the time t2 it takes to get there. Part 3: How long will it take for the cannonball to fall from the top of its trajectory y2 to the height of the ship?
A pirate ship is rapidly approaching your fort! You bravely station yourself at the mounted cannon but find to your dismay that you have only one cannonball. Not only this, yoour cannon is rusted in place and can only fire at an angle theta = 10.0 degrees up from the horizontal. To prevent a siege on your fort, you must fire your cannon at exactly the correct moment to strike the enemy ship at the base of its mast. You know that your cannon is stationed on a wall a height h = 8.00 m above your target , and that it fires at a speed of v1 = 205 m/s. You will use this information to determine the distance d at which the pirate ship is in your cannon's range.
Part 1: Determine the initial vertical velocity v1,y and the initial horizonal velocity v1,x of the cannonball.
Part 2: If the cannonball starts its trajectory at a height y1 = h, determine its height y2 at the top of its arc and the time t2 it takes to get there.
Part 3: How long will it take for the cannonball to fall from the top of its trajectory y2 to the height of the ship?
Part 4: Determine t3, the time the cannonball is in the air between being fired and striking the ship. From this and your answer for v1, x, determine the optimal distance d of the ship from the wall.
Part 5: Check your final answer for reasonableness. Do the units make sense? Is the distance d that you found a reasonable distance to be able to see from atop a wall of height h? Hint: when you are standing on the beach, the horizon is 3 miles away.
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