## 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.