kinematics help

[CJPowell27]

Hey guys I've been stuck on a physics equation for like 20 minutes and I was wondering if someone could help.  

The problem is asking for "at what height was the ball shot from."  I found the time of flight to be 1.35 Seconds and I can't get the height

A 7kg ball is shot horizontally at a velocity of 6m/s. It lands 8.1316m away from the spot in which it was shot. Air resistance is negligible.

What is the time of flight?  

Thanks, CJ

[Pugs501]

The Answer with how I did it is.

[Vacsol]

8.93m

[CJPowell27]

-oops-

Can I ask you solved it?

Thanks

[Vacsol]

Can I ask you solved it?

Thanks

t = 1.35

a =  9.8

 

D = V_i*t+.5at²

 

D = 0t+4.5(1.35²)

 

D = 4.5(1.8225)

 

D = 8.20m

[danpaq]

You aren't exactly correct.  The calculation of flight duration is perfect.

 

EDIT:

Well the individual above me updated his calculation, however what I state here still holds value. The member above me approximated g to be 9.0 m/s when it equals 9.81 m/s at "sea level". Please note scientists approximate gravity to be 10m/s. Round up, not down!!!!

He used the following equation previously: v = dt * a to be used as reference so my language below makes sense.

Please check your dimensions in the latter equation:  ( seconds ) x ( meters / second / second ) = ( meters / sec ) ... this is a velocity you solved for.  The velocity it collides into the ground with to be exact.

 

Assuming a object flying in a vacuum free falls for 1.35 seconds...

x = x₀ + v₀Δt + ½aΔt²

That's the equation you want.  The Xo and Vo terms are zero, so all you are left with is...

x = ½aΔt²

 

Substitute g = 9.8 in for a and you are left with........

x = .5 * 9.8 * 1.35²

x = 8.90325 m

 

To check our answer it is a good habit to check dimensions once again.

m =? 1 * (m/s/s) * (s*s)

m = m

(remember the 0.5 is dimensionless)

 

Yes, this does, in fact give us meters as an answer so we can at least pretend it's the right answer  I'm surprised the author didn't pick criteria for the ball to fall equally vertical as it traveled horizontal.

 

Dan.

[CJPowell27]

t = 1.35

a =  9.8

 

D = V_i*t+.5at²

 

D = 0t+4.5(1.35²)

 

D = 4.5(1.8225)

 

D = 8.20m

Could you help with the 5th one too?

[danpaq]

CJPowell may I ask why you are taking this class? Also, I hope you learned from my post. If you would like me to explain how to do these problems I will. But it takes me a little bit of time. If you would like me to continue, please let me know!