Projectiles: 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): angle of 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

Projectiles: 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):  angle of  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

Quizplus · Accepted Answer

Based on the information given in the problem, we know that the projectile lands at the same height it was launched from, which means the angle of launch must be 45 degrees. Using the kinematic equation:

d = vt*sin(2θ)/g

where d is the horizontal distance traveled, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity (9.81 m/s^2).

Substituting the given values and solving for v, we get:

v = d*g/(sin(2θ))

Plugging in the given distance and angle, we get:

v = (11 meters) * (9.81 m/s^2) / sin(90 degrees) ≈ 44 m/s

Therefore, the correct answer is A) 44 m/s.

Projectiles: a Catapult Is Tested by Roman Legionnaires