Equation
y(x) = −(g / 2v₀²cos²θ)x² + (tanθ)x + h₀
Parabolic path of a projectile launched at velocity v₀ and angle θ. Gravity g = 9.8 m/s².
Parameters
Initial Velocity (v₀)
20 m/s
Launch Angle (θ)
45°
Computed Results
Max Height
—
Range
—
Time to Apex
—
Flight Time
—
Equation
A(x) = x · (L − 2x) = Lx − 2x²
Maximize rectangular enclosure against a barn wall. L = fence length, x = perpendicular side. Optimal at x = L/4.
Parameters
Total Fence Length (L)
100 m
Side Length (x)
25.0 m
Computed Results
Current Area
—
Max Possible
—
Optimal x
—
Other Side
—
Equation
PE(x) = ½kx²
Elastic potential energy in a spring. k = spring constant (N/m), x = displacement from equilibrium. Force F = −kx.
Parameters
Spring Constant (k)
50 N/m
Displacement (x)
0.50 m
Computed Results
Potential Energy
—
Spring Force
—
Max PE (x=2m)
—
% of Max
—