Notes on using Projectiles.xls
This spreadsheet allows students to explore the graphs of velocity and displacement for a projectile which is moving under gravity in 2 dimensions.
Background:
The constant acceleration equations and acceleration due to gravity.
The idea of the horizontal and vertical components of a 2D velocity vector.
Questions for students.
What important modelling assumptions are being made?
How could you calculate the time of flight?
How could you calculate the horizontal range?
Use your method to find the horizontal range for an angle of projection of 35, an initial speed of 40 and a starting height of 0. Repeat with a starting height of 8. Use the spreadsheet to check your answers.
Set the vertical height to zero and for a given speed vary the angle of projection. Which angle gives you the maximum horizontal range?
How is your answer to the previous question affected when the starting height is non zero?
Set non-zero values for the initial speed and angle of projection. Calculate the horizontal component of the initial velocity. Explain why this will remain constant during the flight.
Bearing in mind your answer to the previous point what is significant about the value of the velocity at the point of maximum vertical height?
How could the maximum height be calculated?
Calculate the maximum height for an angle of projection of 60, an initial speed of 40 and a starting height of 10. Use the spreadsheet to check your answer.
For a zero starting height investigate what values of the initial speed and angle of projection would achieve a particular horizontal range (say 150). How is this affected if the starting height is non zero? Try to explain your findings mathematically.
Calculate the possible angles of projection to achieve a horizontal range of 150 with an initial speed of 40 and a starting height of 0. Use the spreadsheet to check your answers.
For an angle of projection of 75, an initial speed of 40 and a starting height of 0 find the speed with which the particle would hit the ground. What do you notice?
Now set the starting height to 20. Calculate the speed with which the particle hits the ground.