# Projectiles in GeoGebra

#### Part 1 Introduction to animation

Dowload and install GeoGebra from the GeoGebra website.

In GeoGebra you can define the position of a point on a graph by an equation but first the variables in the equation must be defined. The variables are changed using a slider so click the slider control

then place the slider somewhere on the graph where it won't get in the way by clicking in that place.

This variable is going to be time so call it t and choose the range between 0 and 5.

Add a second slider for the variable, v for velocity.

To add a point to the graph click the New point button then place the point somewhere on the graph by clicking in that place

The coordinates of the point will be displayed in the algebra window on the left. It is listed as a free object since you haven't assigned any values to it yet.

The next stage is to write the equation that will define the position,s of the point at different times. We will take the velocity to be constant so s=vt. Write this equation in the input box at the bottom of the screen then enter (use * for multiply). s now appears as a dependent object. To make the position of the point vary with time replace the x coordinate with the letter s. The position will now change as you move the slider for t.

To animate the point choose the pointer then double click the slider. Choose the basic tab and tick a "animation on".

The point will now move back and forth as the time changes. To make it only go forwards choose the slider" tab and then"increasing" from the animation options. The whole process is shown in the screen cast below.

#### Part 2 projectile motion.

Projectile motion has rather more variables than simple one dimensional constant velocity so you first need to make a slider for each variable.

Time t

Angle α

Velocity v

Acceleration g

Now write the equations that relate the horizontal and vertical displacements in the input bar at the bottom.

(horizontal displacement) v*cos(α)*t

(vertical displacement) v*sin(α)*t + 0.5*g*t^2

These will be assigned the letters a and b after you click enter.

Place a point on the graph and replace the (x,y) coordinates with (a,b).

Start the animation and play with the variables as before. To leave a trace behind the projectile right click the point and click "trace on".

In my version of the simulation I added a cannon and ship, you'll have to work out how to do that yourself.