At what velocity does the cannonball leaves the cannon?

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To determine the velocity at which a cannonball leaves a cannon fired at a 45-degree angle and traveling 500 meters, the relationship between horizontal and vertical components of motion is crucial. The horizontal distance can be calculated using the equation t = 500/(vi*cos45), where t represents time. The vertical motion can be analyzed using dy = viy(t) + 4.9(t)^2, where viy is the initial vertical velocity. The discussion emphasizes that understanding the time of flight is key to finding the initial velocity in the vertical direction. Ultimately, the problem requires solving for the initial velocity based on the given parameters.
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Yeah I cannot figure this out...

Homework Statement



.A cannon fires a cannonball 500.0m downrange when set at a 45.0o angle. At what velocity does the cannonball leaves the cannon?

Given Angle : 45
Distance: 500m
Vi : ?

Homework Equations



dy = viy(t)+ 4.9(t)^2

The Attempt at a Solution



Only thing I figured out is that vix = viy

and that t = 500/vicos45
 
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so if you know how long it was in the air, how long did it take the cannonball to get to its max height

if you know how long it took to get to the max height, then you can get the initial velocity in the y direction from that
 
SHISHKABOB said:
so if you know how long it was in the air, how long did it take the cannonball to get to its max height

if you know how long it took to get to the max height, then you can get the initial velocity in the y direction from that

I think time is irreleavent here...
 
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TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

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