Answer:
The rock will rise 2.3 m above the top of the window
Explanation:
The equations for the position and velocity of the rock are the following:
y = y0 + v0 · t + 1/2 · g · t²
v = v0 + g · t
Where:
y = height of the rock at time t
v0 = initial velocity
y0 = initial height
g = acceleration due to gravity
t = time
v = velocity at time t
If we place the center of the frame of reference at the bottom of the window, then, y0 = 0 and at t = 0.22 s, y = 1.7 m. With this data, we can calculate v0:
1.7 m = 0.22 s · v0 - 1/2 · 9.8 m/s² · (0.22 s)²
Solving for v0:
v0 = 8.8 m/s
Now that we have the initial velocity, we can calculate the time at which the rock reaches its maximum height, knowing that at that point its velocity is 0.
Then:
v = v0 + g · t
0 = 8.8 m/s - 9.8 m/s² · t
-8.8 m/s / -9.8 m/s² = t
t = 0.90 s
Now, we can calculate the max height of the rock:
y = y0 + v0 · t + 1/2 · g · t²
y = 8.8 m/s · 0.90 s - 1/2 · 9.8 m/s² · (0.90 s)²
y = 4.0 m
Then the rock will rise (4.0 m - 1.7 m) 2.3 m above the top of the window
