Question

How do parameters such as initial height, initial angle, and altitude affect the trajectory of an object?

Answer 1

A projectile motion is described by the position vector:

`\vec{r}=\lbrack x_0+(v\cos \theta)t\rbrack\hat{i}+\lbrack y_0+(v\sin \theta)t-(1)/(2)gt^2\rbrack\hat{j}`

where v is the initial velocity, theta is the intiial angle, x0 is the inital horizontal distance, y0 is the initial height, g is the acceleration of gravity and t is the time.

From the trajectory described above we can conclude the following for the parameters:

• If the inital velocity and initial height are fixed then we conclude that the larger the initial angle the longer the time of flight of the object and the larger the maximum height.

,

• For a fixed angle and initial height the larger the velocity the larger the range of the object and maximum height.

,

• For a fixed initial angle and velocity the larger the initial height the larger the maximum height of the object.

Now, all of this parameters affect the range, maximum height and time of flight of the object; this means that if vary one the previous properties will change but individually they change according to the list above.