Cannonball
Let's fire a cannon. Recall the general equation for projectile motion. The height metres of the ball whose horizontal distance is metres away is given by the equation
where , , and . Here, denotes the initial speed, denotes the initial height, denotes the gravitational constant on earth, and denotes the angle of elevation.
The cannon fires from ground level at a initial speed of .
Question 1. Write down the values of and .
Create a GeoGebra simulation given your values of and in the previous part by entering the following commands into the input bar. Press ENTER after each input.
- T = Slider(0.1, 89.9, 0.1)
- S = T * pi / 180
- g = 9.81
- a = g / (200 * (cos(S))^2)
- b = tan(S)
- c = 0
- y = a*x^2 + b*x + c
Cannonball
Question 2. Fix . What is the horizontal distance that the cannonball travels?
Question 3. Find a different value of that gives the same horizontal distance.
Question 4. Find the value of that maximises the horizontal distance.
Bonus Question. Why does this happen?