Help me figure out where this equation was derived

[d3111]

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

 

[Mentallic]

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?

 

[kerimek]

The equation t = delta x / (vi * cos theta) is known as the time of flight equation and is derived from the kinematic equations of motion. In this case, t represents the time it takes for the football to reach its peak height, delta x represents the horizontal distance traveled by the football, vi represents the initial velocity, and cos theta represents the cosine of the angle at which the ball was kicked. This equation is used to calculate the time it takes for an object to reach a certain distance when launched at a specific angle and initial velocity. It is a fundamental equation in projectile motion and can be derived using basic principles of physics such as Newton's laws of motion and conservation of energy. I hope this helps clarify where the equation comes from.