How can I use the range equation to find the initial velocity of a projectile?

[Havenater23]

1. A football is kicked so that is had a hang time for 4.6 s and hits the ground 23m down the field ?
What was the velocity of the football when it was kicked?
2. I used the Dx=Vx(t), don't know what to use after that.
3. Can someone show step by step how to get this, I'm having trouble trying to get an answer.
Can anyone just show me the equation I would use after that. I know I can find the xi and xf , but how do I find the yi or yf?

 

[wrong_class]

Think about this problem in terms of components:

hang time is vertical, distance is horizontal. you should also used the equation Dy(t) = -.5at^2 + Vit + y0. from there, you can get the y component, then just find sqrt(Vx^2 + Vy^2)

 

[Havenater23]

Well this is how I set it up, similar to yours : dy= vi(t) + 0.5(a)(t)^2

I did that have got this: dy= vi(4.6) + 103.684
I didn't take into consideration that 9.8 is negative so sorry
But where do I go from there, I don't know how to solve the rest

 

[wrong_class]

You know the x distance: x0 = 0, xf = 23m, so 23 = Vx * t gives you Vx
you have the y time: solve for Vy with 0 = Dy(t). there will be 2 answers: 0 and the Vy you are looking for

 

[Havenater23]

Yeah, I know about competent breakdown. I got like 22.9 m/s for the Viy.I tested it using the range equation and it worked well. Thank you so much , it really did help me !