A catapult is tested by Roman legionnaires. They tabulate the results in a papyrus and 2000 years later the archaeological team reads (distances translated into modern units): Range = 0.20 km; angle of launch = π/4; landing height = launch height. What is the initial velocity of launch of the boulders if air resistance is negligible?
A) 44 m/s
B) 1.4 m/s
C) 22 m/s
D) 0.69 m/s

Question

Quizplus · Accepted Answer

The range R of a projectile launched at an angle θ with initial velocity v is given by R = (v^2 * sin(2θ)) / g. Given R = 0.20 km = 200 m, θ = π/4, and g = 9.8 m/s², solving for v gives v = sqrt(R * g / sin(2θ)) = sqrt(200 * 9.8 / sin(π/2)) = 44 m/s.

A Catapult Is Tested by Roman Legionnaires