Problem 12 - ball thrown vertically
What must be the initial speed of a ball thrown vertically from ground level to rise to a maximum height of 20m. How long it will be in the air?
Given:
h = 20m – maximum height,
g = 9.81m/s2 – gravitational acceleration is usually assumed as known.
We are looking for:
v0 = ? – initial speed required,
t = ? – time of being in the air.
This time is equal to the sum of rising time t1 and falling time t2. From the “Free fall” paragraph we know, that t1 = t2, so
t = 2t1.
We write two equations,
h = v0t1 - (1/2)gt12 (1) distance traveled
0 = v0 – gt1 (2)
Final speed at maximum height is ZERO, the ball stops for an instant when changing the direction of motion from rising to falling.
From Eq.2
t1 = v0/g
Substituting this into Eq.1 we have
and from this relation we find
Substituting this v0 into Eq.2 and solving with respect to t1 we have
Substituting numbers given in the problem, we get
v0 = 19.8m/s
t = 2t1 = 4.4s
which is the final answer to the questions posted in problem.