Question

How do you calculate the initial speed given time and displacement?

The question is: The longest kick in CFL history was 83.2m. If the ball remained in the air for 4.12s, determine its initial speed.
I calculated it several times and got the same answer, 40.38m/s, but the textbook says it's 28.6m/s.

Answer 1

Let's first find the velocity in the x-direction which is constant.

`d = vt \\ v = (d)/(t) \\v = (83.2m)/(4.12s) \\ v= 20.2m/s`

Now, we need the velocity in the y-direction

`d = v_(o)t + (1)/(2)a t^(2) \\ d - (1)/(2)at^(2) = v_(o)t\\v_(o) = (0 - (1)/(2)(-9.81)(4.12)^(2))/(4.12)\\v_(o) = 20.2m/s`

Finally, we need to put the two velocities together using pythagorean theorem

`v_(t)^(2) = v_(x)^(2) + v_(y)^(2)`

`v_(t) = \sqrt{20.2^(2) + 20.2^(2)}`
v = 28.6m/s