Loops are very useful for doing the same calculation over and over, very quickly.

In this problem, we will use a loop to call a function with different inputs, and store the result in an array.

You are doing an experiment where you are trying to experimentally calculate the air resistance on falling objects. To calculate this resistance, you build an apparatus that will release objects with different initial velocities at different distances. You also set up a system for measuring the exact time it takes each object to fall.

To do your air resistance calculation, you need a theoretical comparison for the amount of time it takes an object to fall in a vacuum. Thankfully you already have that function (please download fallTime. m from Canvas)! What you do not have yet is a way to call that function repeatedly for all of the distance and velocity data you have!

Write a function called timeLoop. It should take two inputs, arrays for initial velocity and distance. These two input arrays will always have equivalent lengths, as the indices of these arrays correspond to the same data point from your experiment. It should return one output, an array for the theoretical amount of time it would take for the object moving at that initial velocity to fall that distance. To accomplish this task, you should call fallTime. m inside of a loop.

For example, if you called timeLoop with the input array [2 -3 5] for initial velocities (negative numbers mean the object was moving upwards initially) and [100 150 300] for distances, your function call and resulting output would look like this:

IN Matlab

%This function calculates how long it takes an object to fall a certain
%distance given a certain initial velocity and a distance

function time = fallTime(startVelocity, distance)

g = 9.81; %m/s^2

finalVelocity = sqrt(startVelocity^2 + 2*g*distance); %m/s

time = (finalVelocity - startVelocity)/g; %s