Help me figure out where this equation was derived

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The discussion centers on deriving the equation t = Δx / (vi * cosθ) for calculating the time it takes for a football to travel a horizontal distance when kicked at an angle. The poster has already solved a related problem but seeks clarification on the origin of this specific equation. It is explained that the time for an object moving at uniform speed to cover a distance is calculated using t = Δx / u, where u is the horizontal component of the initial velocity. The horizontal velocity is determined by multiplying the initial velocity (vi) by the cosine of the launch angle (θ). Understanding this derivation is crucial for solving projectile motion problems effectively.
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Homework Statement



A placekicker must kick a football from a point 36.0 m (about 40 yards) from the goal, and half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 23.0 m/s at an angle of 46.0° to the horizontal.

I have completed the problem correctly but was told to find time by t= delta x / (vi *costheta)

Where is this equation derived from is what I'm asking?

thanks
 
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The time (t) it takes for something with uniform speed (u) to complete some displacement (\Delta x) is given by t=\frac{\Delta x}{u}. But the problem is that the uniform speed isn't quite the initial velocity of the ball. The ball is projected at an angle to the horizontal, so can you figure out what the horizontal velocity of the ball is?
 

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