example 2 - free fall\n\na stone is thrown upward with an initial velocity of 30 m/s.\na) how high above the…

example 2 - free fall\n\na stone is thrown upward with an initial velocity of 30 m/s.\na) how high above the point of release will the stone rise?\nb) what will be the velocity of the stone when it returns to your hand?\nc) for how long will the stone remain in the air?
Answer
Explanation (a):
Step1: Known quantities and equation
u=30 m/s, v=0 m/s, a=-9.8 m/s², use (v^2 = u^2 + 2as)
Step2: Calculate height
(s=\frac{v^2 - u^2}{2a}=\frac{0 - 30^2}{2\times(-9.8)}=\frac{-900}{-19.6}\approx45.92\ \text{m})
Answer (a):
≈45.92 m
Explanation (b):
Step1: Free fall symmetry
Return speed = initial speed, direction opposite
Step2: Determine velocity
Velocity is -30 m/s (downward)
Answer (b):
-30 m/s
Explanation (c):
Step1: Displacement s=0, use (s = ut + \frac{1}{2}at^2)
(0 = 30t - 4.9t^2\Rightarrow t(30 - 4.9t)=0)
Step2: Solve for total time (t≠0)
(t=\frac{30}{4.9}\approx6.12\ \text{s})
Answer (c):
≈6.12 s