how to write a code to determine the times at which ball hits the floor for the first eight bounces, letting t= 0 be when ball is dropped.?

how can i code this problem ?? A ball that is dropped on the floor bounces back up many times, each time at a lower height than the previous bounce. Suppose that the rebound velocity of a rubber ball is 0:75 times the impact velocity. It can be shown that the velocity with which a ball hits the floor after falling h meters is given by v =(2gh)^(1/2). where g = 9:81m=s2 is the acceleration due to gravity. The time between successive bounces is given by t = v=g, where v is the upward velocity after the last impact. If such a ball is dropped from a height of 2:5m, determine the times at which the ball hits the floor for the first eight bounces, letting t = 0 be when the ball is dropped. (Derive a formula for the rebound velocity after each bounce as a function of the bounce number based on the previous information. Create a vector n = 1,2,... ,8 and use the formula to calculate a vector of rebound velocities. Then calculate a vector of times between each bounce and add them up using sum

Answer 1

[Image Analyst]

The distance formula is d = d0 + v*t + a*t^2/2. So when it's launched off the ground d0=0, and when it lands d=0, and the acceleration is a=-g where g=+9.8, so the formula is 0=v*t-g*t^2/2, or g*t^2/2 = v*t, or g*t/2 = v, or t = 2*v/g. (Looks like this differs from your "t = v=g" formula, whatever that is, so be sure to verify the correct formula.)

So just put this in a for loop over v

v(1) = .....
for bounceNumber = 1 : 8
    bounceTimes(bounceNumber) = ......  % Time from bounceNumber to (bounceNumber + 1)
    % Update v for the next bounce
    v(bounceNumber+1) = ..... some function of old v......
end
totalTime = sum(..........

I think this should be enough hints.