Abstract

Citation

Researchers should cite this work as follows:

• Winkel, B. (2022). 3-042-CatapultLaunch-ModelingScenario. SIMIODE, QUBES Educational Resources. doi:10.25334/JRPS-5H67

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Article Context

Description

A projectile is fired from a catapult. The angle of elevation above the horizontal for the launch is alpha (in radians or degrees). For a given speed v₀ the initial velocity is v(0) = <v₀ cos(alpha), v₀ sin(alpha)>. You should verify this. The initial launch position is (x₀,y₀).

We use g as the acceleration due to gravity (either 32 ft/sec² or 9.81 m/sec²). The functions x(t) (down range)and y(t) (height) describe the coordinates of the projectile at time t in seconds. Let us not take into consideration air resistance. If we did how would the trajectories change?

The distance that a catapult fires a projectile depends on two factors: (1) the projectile's initial velocity v₀ and (2) the angle of elevation, alpha, of the launch of the projectile from horizontal. Suppose you can give the projectile an initial velocity of v₀ = 300  ft/sec.

Investigate the effects of varying the angle of elevation from the horizontal on the horizontal range of the projectile. What angle maximizes this range?