For a numerical approximation, maybe you can try this.
First some background information of Physics here. The first derivative of y is speed, and the second derivative of y is acceleration.
Now depending on what accuracy you want to get, pick a small time period (delta_t). Start with delta_t = 1 second first for example. Adjust it later.
Here is the approach.
- For each time period, speed determines how far it drops. Acceleration determine how speed increases.
- Assuming for a short time period, speed is constant, acceleration is constant for approximation, so we can easily compute how y increases and how speed increases.
Look at the first several seconds for example:
- The first second, Initial speed is 0, so it does not drop in the first second (again this is an approximation), accelaration is -9.8 m/s^2. Speed increases to -9.8m/s.
- The second second, now speed is -9.8m/s, so it drops 9.8m. Acceleration is (0.023/87)*(-9.8)^2 - 9.8. So the speed is acceleration*1sec-9.8m/s.
Repeat the above steps and accumlate the distance it drops. Once the accumulation reaches 3000m, you get the time and the speed.
You can see this approach, the accuracy of time is 1sec. To get to higher accuracy, you need to decrease delta_t, and of course it will take a longer time to find the (better) answer.