A stone is thrown vertically upwards and it reaches a maximum height of 30m. What was its initial velocity?
A stone is thrown vertically upwards. So that the only force acting on the stone is the Gravitational force . we consider the the upward directions as positive y-axis . Then there is no motion is along x-axis. And the acceleration of the stone is -g
where g is acceleration due to gravity
the negative indicates that the acceleration is along negative y-axis (towards downward direction).
The equation of motion connecting the velocities and the displacement of the particle is given by
v is the final velocity,
u is the initial velocity( velocity with which the stone is thrown)
a is the acceleration . here (-g, acceleration due to gravity),
S is the displacement . here(Maximum Height reached by the stone)
At the maximum height velocity becomes zero ( v=0)
SUBSTITUTE VALUES IN THE EQUATION
Therefore the velocity with which the stone thrown is