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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.

Verified Answer :

chipperrider

Let's first find the velocity in the x-direction which is constant.
\(d = vt \\ v = \frac{d}{t} \\v = \frac{83.2m}{4.12s} \\ v= 20.2m/s\)

Now, we need the velocity in the y-direction
\(d = v_{o}t + \frac{1}{2}a t^{2} \\ d - \frac{1}{2}at^{2} = v_{o}t\\v_{o} = \frac{0 - \frac{1}{2}(-9.81)(4.12)^{2}}{4.12}\\v_{o} = 20.2m/s\)

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

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