Catapult Project
Derive the equation of the path of your projectile using math and physics.
(1) 𝒗 = 𝒗𝟎 + 𝒂𝒕
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𝟏
(2) 𝒅 = 𝒅𝟎 + 𝒗𝟎 𝒕 + 𝟐 𝒂𝒕𝟐
*Velocity at any given point = initial velocity + (acceleration)(time to peak)
(Plug in zero, no velocity at top)
(-32 feet gravity)
*Vertical distance = Initial height + initial velocity(time to peak) + ½ (acceleration)(time to peak)2
(to peak)
(use zero on ground) + (get from other equation)
(-32 feet gravity)
1) Using equation (1) from above, solve for the initial velocity(𝒗𝟎 ) of your projectile.
2) Using equation (2) from above, find the maximum height of your projectile.
(Remember, the initial height will be zero and use -32 for acceleration. Time and initial
velocity will be dependent on your catapult.)
3) Write the equation of your parabola in vertex form. (Use the vertex form of a parabola,
𝒚 = 𝒂(𝒙 − 𝒉)𝟐 + 𝒌, with your vertex to solve for a, then rewrite.)
4) Convert your equation from vertex form to standard form 𝒚 = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄.
5) Compare the standard form of a parabola (𝒚 = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄) to the kinematic equation from
𝟏
above(𝒅 = 𝒅𝟎 + 𝒗𝟎 𝒕 + 𝟐 𝒂𝒕𝟐 ). Pair each variable in the first column with its corresponding variable
in the second column.
𝒚 = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄
𝟏
𝒅 = 𝒅𝟎 + 𝒗𝟎 𝒕 + 𝒂𝒕𝟐
𝟐
Give a brief
statement
explaining how you
determined which
letters correspond.
y
x
a
b
c
6) Solve the quadratic equation using the quadratic formula.
Explain what each
variable in equation
two represents.
7) Solve the quadratic equation using graphing technology. Compare your answer to the answers
from question #6.
8) Graph your quadratic equation. Label the vertex and the x-intercepts.