Answer:
a) v = 15.6 m/s
b) 0.65 s are needed to reach a height of 12.3 m
Explanation:
The equations that describe the height and velocity of the stone are the following:
y = y0 + v0 · t + 1/2 · g · t²
v = v0 + g · t
Where
y = height of the stone at time t
y0 = initial height
v0 = initial speed
t = time
g = acceleration due to gravity
b) First, let´s find the time at which the stone reaches a height of 12.3 m:
y = y0 + v0 · t + 1/2 · g · t²
12.3 m = 0 m + 22.0 m/s · t + 1/2 · (-9.8 m/s²) · t² (y0 = 0 placing the center of the frame of reference at the point at which the stone is thrown.)
-4.9 m/s² · t² + 22.0 m/s · t - 12.3 m = 0
t = 0.65 s (when the stone goes upward) and t = 3.84 s ( when the stone returns downward) .
So, 0.65 s are needed to reach a height of 12.3 m
a) The velocity at that time will be:
v = v0 + g · t
v = 22.0 m/s - 9.8 m/s² · 0.65 s = 15.6 m/s
