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Vector representations of motion are useful because a vector captures information on direction, and not just speed.
For example, here are two vectors, each describing a projectile that has a speed of 3. In the first one, it is moving along the positive x-axis (3i). In the second, it's moving along the positive y-axis (3j).. Vectors typically use an i,j,k notation to indicate motion along x,y,z axes respectively.
V = 3i + 0j
V = 0i + 3j
The path of a projectile has components in both the horizontal direction (how far is it downrange) and vertical direction (how high is it). These can be treated independently, as a function of time.
So, you have on parametric expression that describes position, velocity, acceleration, etc along the x-axis (horizontal motion) as a function of time, and another expression that describes position, velocity, acceleration, etc along the y-axis (vertical motion)
Parametric representations allow you to break apart a complex motion and independently describe the motions along the x, y an z axes separately as a function of a common parameter. Typically this would be time, in projectile motion problems.
The maximum height of a projectile is based on its initial launch angle and inital velocity (ignoring wind resistance and other effects).
The equation is
H = [ (Vo * sin(LA))^2 ] / (2 * g)
Where
H = height (meters)1
Vo = launch velocity (meter/sec)
LA = Launch angle (straight up = 90 degrees, horizontal = 0 degrees)
g = gravity (9.8 meter/sec^2)
Check out the link below for other equations describing ideal projectile motion including flight time, range, time in the air, etc.
Hope this helps,
-Guru
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