You throw a ball straight down from an apartment balcony to the ground below. The ball has an initial velocity of 4.50 m/s, directed downward, and it hits the ground 2.04 s after it is released. Find the height of the balcony.
twenty....2m/s(2.4)(5.40)....
To find the height of the balcony, we can use the kinematic equation:
h = (1/2)gt^2 + v_0t + h_0
where:
h = height of the balcony
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken (2.04 s)
v_0 = initial velocity (4.50 m/s)
h_0 = initial height (which we want to find)
Since the ball is thrown straight down, the initial velocity, v_0, is negative (-4.50 m/s) because it is directed downward.
Rearranging the equation, we have:
h_0 = h - (1/2)gt^2 - v_0t
Now we can substitute the known values into the equation:
h_0 = 0 - (1/2)(9.8 m/s^2)(2.04 s)^2 - (-4.50 m/s)(2.04 s)
Simplifying this expression will give us the height of the balcony (h_0).