Question

There’s two rocks. On of them is at the height of 125m from earth and is going to start falling. The other was thrown up with a speed of 50 meters per second. When at what height will they meet? (Sorry if there are mistakes English isn’t my native language)

Answer 1

The equations of motion of rocks are given by

$$y_1(t)=y_{01}+v_{01}t-gt^2/2\\ y_1(t)=125-4.9t^2$$

$$y_2(t)=y_{02}+v_{02}t-gt^2/2\\ y_2(t)=50t-4.9t^2$$

At the meeting point

$$y_1(t)=y_2(t)$$

$$125-4.9t^2=50t-4.9t^2$$

$$t=125/50=2.5\:\rm s$$

The corresponding height

$$y=125-4.9*2.5^2=94.4\:\rm m$$