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A cannon fires a 10.0 kg cannonball horizontally from the top of a 50 m high cliff with an initial speed of 80.0 m/s. The origin (0,0) is at the base of the cliff as shown in the figure, not at the starting position of the cannonball. Assume no air resistance, ball rotation, etc. Only gravity is acting on the ball while it is in flight. a. Fill in the following table. If there is/are unknown quantity/ies put a question mark in those boxes. Don't forget units! Vxi Vyi Vxf Vyf ax ay (0,0) b. Using the information in the table, determine how long the cannonball is in the air.

A cannon fires a 10.0 kg cannonball horizontally from the top of a 50 m high cliff with an initial speed of 80.0 m/s. The origin (0,0) is at the base of the cliff as shown in the figure, not at the starting position of the cannonball. Assume no air resistance, ball rotation, etc. Only gravity is acting on the ball while it is in flight. a. Fill in the following table. If there is/are unknown quantity/ies put a question mark in those boxes. Don't forget units! Vxi Vyi Vxf Vyf ax ay (0,0) b. Using the information in the table, determine how long the cannonball is in the air.

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**Problem Statement:** c. What is the final position, \(\vec{r}_f\), of the cannonball when it hits the ground? Write your answer in the form of a vector. d. What is the average velocity \(\vec{v}_{ave}\) of the cannonball from the time it is launched to the time it reaches the ground? e. If the cannonball were launched at a 30º angle above the horizontal with the same speed, what would its initial velocity vector be? Fill in the components and show your work. f. Would the cannonball launched at an angle be in flight for a longer time, shorter time, or the same time as the one launched horizontally? Show and/or explain your answer. (If you can explain it well, you don’t have to do any calculations!)
Transcribed Image Text:**Problem Statement:** c. What is the final position, \(\vec{r}_f\), of the cannonball when it hits the ground? Write your answer in the form of a vector. d. What is the average velocity \(\vec{v}_{ave}\) of the cannonball from the time it is launched to the time it reaches the ground? e. If the cannonball were launched at a 30º angle above the horizontal with the same speed, what would its initial velocity vector be? Fill in the components and show your work. f. Would the cannonball launched at an angle be in flight for a longer time, shorter time, or the same time as the one launched horizontally? Show and/or explain your answer. (If you can explain it well, you don’t have to do any calculations!)
A cannon fires a 10.0 kg cannonball horizontally from the top of a 50 m high cliff with an initial speed of 80.0 m/s. The origin (0,0) is at the base of the cliff as shown in the figure, not at the starting position of the cannonball. Assume no air resistance, ball rotation, etc. Only gravity is acting on the ball while it is in flight. ### Table Completion Fill in the following table. If there is/are unknown quantity/ies put a question mark in those boxes. Don’t forget units! | **Variable** | **Initial (i)** | **Final (f)** | |--------------|-----------------|---------------| | x | | | | y | | | | v<sub>x</sub> | | | | v<sub>y</sub> | | | | a<sub>x</sub> | | | | a<sub>y</sub> | | | | t | | | ### Diagram Explanation The diagram shows a cannon on top of a cliff firing a cannonball horizontally. The cannonball follows a parabolic trajectory downwards due to gravity, with a dotted line representing its path. The point (0,0) is marked at the base of the cliff. An arrow labeled **v<sub>i</sub>** indicates the initial horizontal velocity of the cannonball. ### Problem Solving b. Using the information in the table, determine how long the cannonball is in the air. --- This exercise involves applying concepts of projectile motion to determine unknown variables and solve for the time of flight of the cannonball.
Transcribed Image Text:A cannon fires a 10.0 kg cannonball horizontally from the top of a 50 m high cliff with an initial speed of 80.0 m/s. The origin (0,0) is at the base of the cliff as shown in the figure, not at the starting position of the cannonball. Assume no air resistance, ball rotation, etc. Only gravity is acting on the ball while it is in flight. ### Table Completion Fill in the following table. If there is/are unknown quantity/ies put a question mark in those boxes. Don’t forget units! | **Variable** | **Initial (i)** | **Final (f)** | |--------------|-----------------|---------------| | x | | | | y | | | | v<sub>x</sub> | | | | v<sub>y</sub> | | | | a<sub>x</sub> | | | | a<sub>y</sub> | | | | t | | | ### Diagram Explanation The diagram shows a cannon on top of a cliff firing a cannonball horizontally. The cannonball follows a parabolic trajectory downwards due to gravity, with a dotted line representing its path. The point (0,0) is marked at the base of the cliff. An arrow labeled **v<sub>i</sub>** indicates the initial horizontal velocity of the cannonball. ### Problem Solving b. Using the information in the table, determine how long the cannonball is in the air. --- This exercise involves applying concepts of projectile motion to determine unknown variables and solve for the time of flight of the cannonball.
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