You and your friend throw balloons filled with water from the roof of a several story apartment house You simply drop a balloon from rest. A second balloon is thrown downward by your friend 2.1seconds later with an initial speed of 41.6m/seconds. they hit the ground at the same times. how high is the apartment.
To solve this problem, we can use the kinematic equation for the vertical motion of an object:
y = v₀t + (1/2)gt²
Where:
y = height of the apartment (what we're trying to find)
v₀ = initial velocity
t = time
g = acceleration due to gravity (9.8 m/s²)
First, let's find the time it takes for the first balloon to hit the ground. Since it is dropped from rest, its initial velocity is 0 m/s. Therefore, the equation becomes:
y1 = (1/2)gt¹²
Now, let's find the time it takes for the second balloon to hit the ground. The initial velocity of the second balloon is 41.6 m/s, and it is thrown downward 2.1 seconds after the first balloon is dropped. Therefore, the equation becomes:
y2 = 41.6(2.1-t) + (1/2)gt²
Since both balloons hit the ground at the same time, we can set y1 = y2 and solve for t.
(1/2)gt¹² = 41.6(2.1-t) + (1/2)gt²
Now, we can simplify this equation and solve for t.