Question

What is the equation of the parabolic cylinder bounded by the planes x = 1, x = 0, and z = 0 and the function z = 1/2 * y²?

Answer 1

To prove a projectile's trajectory is parabolic, the time 't' derived from the horizontal motion equation is substituted into the vertical motion equation, yielding a simplified quadratic expression in the form y = ax + bx², demonstrating a parabolic path.

Step-by-step explanation:

To prove that the trajectory of a projectile is parabolic, we start with the equations of motion for a projectile in two dimensions:

• x = V0x * t
• y = V0y * t - (1/2)g * t2

Solving the first equation for t gives us t = x / V0x. Substituting this into the second equation for t, we get y = V0y * (x / V0x) - (1/2)g * (x / V0x)2. This simplifies to y = ax + bx2 where a = V0y / V0x and b = -g / (2 * V0x2). These constants represent the initial velocity components and the acceleration due to gravity, illustrating that the trajectory is indeed a parabola.