IDNLearn.com is the place where your questions are met with thoughtful and precise answers. Our experts provide prompt and accurate answers to help you make informed decisions on any topic.

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.


Sagot :

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

Now, we need the velocity in the y-direction
[tex]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[/tex]

Finally, we need to put the two velocities together using pythagorean theorem
[tex]v_{t}^{2} = v_{x}^{2} + v_{y}^{2}[/tex]
[tex]v_{t} = \sqrt{20.2^{2} + 20.2^{2}}[/tex]
v = 28.6m/s