A ball is thrown upward off the top of a 30-meter high building. 10 meters below the top of the roof, is the top of a window, which is 2 meters high. How long (time) does it take for the ball to pass from top to bottom of the window?
What I have so far is:
-10 = v(initial) t - 4.9 t^2
-12 = v(initial) t - 4.9 t^2
How do I solve this question if I don't even have initial velocity?
"How do I solve this question if I don't even have initial velocity? "
You are quite right. You need additional information, for example maximum height attained, time it took to come back to the top of the roof, initial velocity, etc.
On the other hand, the height of the building (30m) is immaterial.
To solve this question, you need to find the initial velocity (v(initial)) of the ball. The key information you have is that the ball is thrown upward off the top of a 30-meter high building.
Let's break down the problem step by step:
Step 1: Find the time it takes for the ball to reach the top of the window.
The ball is thrown upward off the top of a 30-meter high building, and the top of the window is 10 meters below the top of the roof. Since the ball starts at 30 meters above the window, we can use the equation for the position of an object in freefall:
-10 = v(initial) t - 4.9 t^2
In this equation, -10 represents the relative position of the window from the starting point (negative because the window is below the initial position of the ball). 4.9 t^2 represents the vertical position of the ball as it travels upward, assuming a gravitational acceleration of 9.8 m/s^2.
Step 2: Find the time it takes for the ball to reach the bottom of the window.
The top of the window is 2 meters high, and the ball has to travel 12 meters (from -10 to -2) to reach the bottom of the window. We can use the same equation as in Step 1:
-12 = v(initial) t - 4.9 t^2
Step 3: Solve for the initial velocity (v(initial)).
Since both equations have the same v(initial) and t terms, you can set them equal to each other and solve for v(initial):
-10 = v(initial) t - 4.9 t^2
-12 = v(initial) t - 4.9 t^2
By subtracting the second equation from the first equation, you can eliminate the -4.9 t^2 term:
-10 - (-12) = (v(initial) t - 4.9 t^2) - (v(initial) t - 4.9 t^2)
Simplifying:
2 = 0
Since 2 does not equal 0, this means there is no solution for the initial velocity (v(initial)) that satisfies both equations simultaneously. Therefore, you cannot determine the time it takes for the ball to pass from the top to the bottom of the window with the given information.