https phet colorado edu en simulations projectile motion OBJECTIVES Draw motion diagrams for a projectile launched at an angle Investigate how range, maximum height and flight time of a projectile changes with the launch angle Determine gravitational field strength at a location by using a projectile and performing curve fitting on linearized data PROCEDURE Click on the Vectors window Deselect Air Resistance Air resistance will remain zero for this experiment Mass and diameter of the cannonball will also remain fixed at default values Part 1 Motion Diagrams (questions will be graded) Select the Velocity Vectors in the vectors box and choose Components from the radio buttons Keeping rest of the settings on default, fire the projectile and observe how the vectors change as the projectile falls to the ground a) Draw a motion diagram showing velocity components at different locations b) What happens to the velocity y component at the peak of the projectile Explain why c) What is your observation about initial velocity y component (at the moment of launch from the cannon) to final velocity y component (at the moment when the projectile hits the ground) Discuss any similarity and or difference Now keeping the Velocity Vectors selected, choose Total from the radio buttons Fire the projectile and observe how the velocity vector changes as the projectile falls to the ground a) Draw a motion diagram showing the velocity vector at different locations b) How do the magnitude and direction of the velocity vector change as the projectile moves c) What can you say about the velocity vector at the peak of the projectile d) How is the velocity vector related to the path of the projectile (i e how is this vector drawn in relation to the path) e) Compare initial velocity vector (at the moment of launch from the cannon) to final velocity vector (at the moment when the projectile hits the ground) Discuss any similarity and or difference Now choose the Acceleration Vectors and Force Vectors in the vectors box and keep Total selected from the radio buttons Fire the projectile and observe how the acceleration and force vectors change as the projectile falls to the ground a) Draw a motion diagram showing the acceleration vector at different locations b) Are the acceleration and force vectors related in your observation Part 2 Effects of launch angle on the motion of projectile Reset the simulation and deselect Air Resistance Air resistance will remain zero for this experiment Set initial speed to 15 m s For constant values of initial speed (15 m s), fire the projectile for 8 different angles (25, 35, 45, 55, 65, 75, 85, 90 degrees) Using the Time, Height and Range tool, collect data in the following data table Time, Height and Range tool is accessible in the top right corner of the simulation and looks like this Measure the following quantities R Range (at the location where projectile hits the ground) T f Flight Time (at the location where projectile hits the ground) H Maximum Height (at the peak of the projectile) T h Time at Max Height (at the peak of the projectile) Launch Speed v x (m s) Launch Angle (degrees) Range R (m) Flight Time T f (s) Max Height H (m) Time to Max Height T h (s) sin sin 2 sin 2 15 25 15 35 15 45 15 55 15 65 15 75 15 85 15 90 Using the data table, answer the following questions a) For which angle is the maximum height H of the projectile greatest Explain why b) For which angle is the flight time T f of the projectile greatest Explain why c) For which angle is the range R of the projectile greatest Explain why d) How is the flight time T f of the projectile related to the time to maximum height T h What does it tell us about the projectile motion ( HINT for parts a, b c above For constant value of magnitude of initial velocity i e 15 m s, the components of initial velocity change with launch angle ) Flight time a projectile launched at an angle is given by Explain how you can graphically obtain gravitational field strength g, by plotting T f vs sin Use this graph to calculate g and compare it with known value of 9 81 m s 2 ( plot graph here ) Maximum height of a projectile launched at an angle is given by Explain how you can graphically obtain gravitational field strength g, by plotting H vs sin 2 Use this graph to calculate g and compare it with known value of 9 81 m s 2 ( plot graph here ) Range of a projectile launched at an angle is given by Explain how you can graphically obtain gravitational field strength g, by plotting R vs sin 2 Use this graph to calculate g and compare it with known value of 9 81 m s 2 (plot graph here )

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https://phet.colorado.edu/en/simulations/projectile-motion OBJECTIVES: Draw motion diagrams for a projectile launched at an angle Investigate how range, maximum height and flight time of a projectile changes with

https://phet.colorado.edu/en/simulations/projectile-motion

OBJECTIVES:

Draw motion diagrams for a projectile launched at an angle
Investigate how range, maximum height and flight time of a projectile changes with the launch angle
Determine gravitational field strength at a location by using a projectile and performing curve fitting on linearized data

PROCEDURE:

Click on the Vectors window. Deselect Air Resistance. Air resistance will remain zero for this experiment. Mass and diameter of the cannonball will also remain fixed at default values.

Part 1 - Motion Diagrams (questions will be graded)

Select the Velocity Vectors in the vectors box and choose "Components" from the radio buttons. Keeping rest of the settings on default, fire the projectile and observe how the vectors change as the projectile falls to the ground. a) Draw a motion diagram showing velocity components at different locations. b) What happens to the velocity y-component at the peak of the projectile? Explain why? c) What is your observation about initial velocity y-component (at the moment of launch from the cannon) to final velocity y-component (at the moment when the projectile hits the ground)? Discuss any similarity and/or difference.
Now keeping the Velocity Vectors selected, choose "Total" from the radio buttons. Fire the projectile and observe how the velocity vector changes as the projectile falls to the ground. a) Draw a motion diagram showing the velocity vector at different locations. b) How do the magnitude and direction of the velocity vector change as the projectile moves? c) What can you say about the velocity vector at the peak of the projectile? d) How is the velocity vector related to the path of the projectile (i.e. how is this vector drawn in relation to the path)? e) Compare initial velocity vector (at the moment of launch from the cannon) to final velocity vector (at the moment when the projectile hits the ground)? Discuss any similarity and/or difference.
Now choose the Acceleration Vectors and Force Vectors in the vectors box and keep "Total" selected from the radio buttons. Fire the projectile and observe how the acceleration and force vectors change as the projectile falls to the ground. a) Draw a motion diagram showing the acceleration vector at different locations. b) Are the acceleration and force vectors related in your observation?

Part 2 - Effects of launch angle on the motion of projectile

Reset the simulation and deselect Air Resistance. Air resistance will remain zero for this experiment. Set initial speed to 15 m/s. For constant values of initial speed (15 m/s), fire the projectile for 8 different angles (25, 35, 45, 55, 65, 75, 85, 90 degrees). Using the Time, Height and Range tool, collect data in the following data table. Time, Height and Range tool is accessible in the top right corner of the simulation and looks like this: Measure the following quantities:

R - Range (at the location where projectile hits the ground)
T_f- Flight Time (at the location where projectile hits the ground)
H - Maximum Height (at the peak of the projectile)
T_h - Time at Max Height (at the peak of the projectile)

Launch Speed v_x (m/s)	Launch Angle (degrees)	Range R (m)	Flight Time T_f (s)	Max. Height H (m)	Time to Max. Height T_h (s)	sin	sin²	sin 2
15	25
15	35
15	45
15	55
15	65
15	75
15	85
15	90

Using the data table, answer the following questions: a) For which angle is the maximum height H of the projectile greatest? Explain why? b) For which angle is the flight time T_f of the projectile greatest? Explain why? c) For which angle is the range R of the projectile greatest? Explain why? d) How is the flight time T_fof the projectile related to the time to maximum height T_h? What does it tell us about the projectile motion? (HINT for parts a, b & c above: For constant value of magnitude of initial velocity i.e. 15 m/s, the components of initial velocity change with launch angle.)

Flight time a projectile launched at an angle is given by: Explain how you can graphically obtain gravitational field strength g, by plotting T_f vs. sin. Use this graph to calculate g and compare it with known value of 9.81 m/s². ( plot graph here.)
Maximum height of a projectile launched at an angle is given by: Explain how you can graphically obtain gravitational field strength g, by plotting H vs. sin². Use this graph to calculate g and compare it with known value of 9.81 m/s². ( plot graph here.)
Range of a projectile launched at an angle is given by: Explain how you can graphically obtain gravitational field strength g, by plotting R vs. sin 2. Use this graph to calculate g and compare it with known value of 9.81 m/s². (plot graph here.)