Very bad projectile?
Classical Mechanics
Level
3
A body is projected horizontally with a speed x find the velocity of the body when it covers equal distances in horizontal and vertical directions
v = 2x
v =
x
v = x/2
v =
x
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1 solution
In the x-direction, the body's velocity is a constant x m/s and travels a distance of x t meters from the projection point. In the y-direction one has y = -(1/2) g*t^2 from kinematics. We are interested in the time when y = xt, or:
xt = -(1/2) g t^2 => t = 2x/g seconds (g = gravitational acceleration).
The body's velocity in the y-direction at this moment computes to:
g = (v - 0) / (2x/g) => v = 2x m/s.
Finally, the body's total velocity is just the resultant of the x and y-velocities, or:
V = sqrt[x^2 + (2x)^2] = x * sqrt(5) m/s.