Question 6.9: Projectile motion A body is projected from the ground with s...
Projectile motion
A body is projected from the ground with speed u and lands on the flat roof of a building of height h. Find the speed with which the projectile lands. [Assume uniform gravity and no air resistance.]
Since uniform gravity is a conservative field with potential energy mgz, energy conservation applies in the form
\frac{1}{2} m| v |^{2}+m g z=E,
where O is the initial position of the projectile and Oz points vertically upwards.
From the initial conditions, E=\frac{1}{2} m u^{2}. Hence, when the body lands,
\frac{1}{2} m\left| v ^{L}\right|^{2}+m g h=\frac{1}{2} m u^{2},
where v ^{L} is the landing velocity. The landing speed is therefore
\left|v^{L}\right|=\left(u^{2}-2 g h\right)^{1 / 2}.
Thus, energy conservation determines the speed of the body on landing, but not its velocity.