Solving Projectile Problem: Initial Velocity from Cliff

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To determine the initial speed of a projectile fired from a 20m cliff at a 30-degree angle, the horizontal distance of 40m must be analyzed using the equation Vi cos(30)t = 40, where t represents the total time of flight. The discussion emphasizes the need for a second equation to address the vertical motion, incorporating gravitational acceleration (g = 9.8 m/s²). Participants suggest that solving for time using the horizontal equation can lead to further insights into the vertical motion. Clarification on the relationship between horizontal and vertical components is crucial for solving the problem. The conversation highlights the importance of integrating both dimensions to find the initial velocity accurately.
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Homework Statement



A cannon is fired at an angle of 30 degrees above the horizontal from a cliff that is 20m above a flat river bottom. What is the initial speed of the projectile if it is found to land 40m from the base of the cliff?



Homework Equations


g = 9.8ms^-2
Vi = initial velocity

The Attempt at a Solution


I know that Vi cos 30t = 40, but does the "t" represent the time taken for the entire projectile motion, or just the upper symmetrical parabolic trajectory? I'm stuck at Vi cos 30t = 40 because what I did after simply didn't make any sense at all.

I've been stuck on this question for days on end, please help me with it! Thanks! :D
 
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The t represents the entire time of flight, from your equation you can actually solve for it. Now how about a second equation for the vertical part of the flight?
 
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