We are asked to find the distance a ball has fallen in two seconds after it has been dropped from a height of 50 meters.
We assume that we can ignore all forces except gravity (e.g. we ignore wind resistance, etc...) We use the falling object model:
On Earth, the height of an object falling due to the force of gravity is given by `h=-4.9t^2+v_0 t+h_0 ` where v nought is the initial velocity and h nought is the initial height above the ground (time in seconds and distance in meters.) Here v nought is zero (the ball is dropped, not thrown) and h nought is 50m. Thus:
` h=-4.9(2)^2+50=30.4"m" `
However, the question was not to find the height at time t=2 seconds, but how far the ball had dropped. Since the initial height was 50m and the height at time t=2 is 30.4m, the distance dropped is 19.6m.