A ball is dropped from a 5.0m high window. Assuming air resistance is negligible, calculate the time taken for it to hit the ground.
It is helpful to break down questions and draw a diagram. Here we know we have a ball that is being dropped, so it will initially be stationary. Gravity will cause it to accelerate towards the ground at 9.8 m/s2, and it has a 5.0m drop. This question concerns the mechanics of an object in motion, so we should suspect that we might be required to use a SUVAT equation of motion. In the question we are given the parameters initial speed u = 0.0 m/s, acceleration under gravity a = g = 9.8 m/s2, and distance to fall s = 5.0 m. Our desired result is the time to fall this distance, t. From SUVAT, we know we have one unknown and unstated variable, final speed before the ball hits the ground v. It seems like a good idea to find an equation linking our known parameters, u, a, and s, with our desired result, t.
Looking at the SUVAT equations, many contain the unknown quantity v. It may seem like a good idea to avoid these. Looking at the equation that doesn't contain v, we see it is: s = ut + 0.5at2. At first glance this seems perfect, it connects our known values s, u and a to our unknown desired result, t. However, looking at the question we see that it contains a t2 and a t. We are unable to solve this equation, so we have to try another approach. Looking at the SUVAT equations, we see that all others contain the unknown final speed, v. That means that we should try to determine v from our known parameters s, u, a but without having to rely upon t in the equation. The only option we have is v2 = u2 + 2as. Plugging in our values for u = 0.0 m/s, s = 5.0 m, a = 9.8 m/s2, we get v2 = 98, or v = 9.9 m/s. By knowing v, we are now free to use the other SUVAT equations to determine t. It is best to pick the simplest equation that will achieve this, which is v = u + at. Rearranging for t gives us t = (v - u)/a, and plugging in our values gives us our result, t = 1.0 s. This may seem much more complicated than simply timing the fall, but the SUVAT equations are versatile and useful, and they allow us to predict behaviour and look into what's going on when it can't be easily measured.
