What Formulas Are Essential for Solving Two-Dimensional Motion Problems?

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Essential formulas for solving two-dimensional motion problems include the equations for horizontal and vertical components of motion, specifically using initial velocity (Vi) and angles. The discussion highlights the principle that two horizontal projectiles dropped simultaneously from the same height will hit the ground at the same time due to gravity acting equally on both, regardless of their horizontal velocities. An example problem involves calculating the initial vertical and horizontal components of a shot put's motion based on its time in the air and horizontal distance traveled. Another example requires determining the launch angle of a golf ball given its horizontal distance and time of flight. The thread emphasizes the need for clarity in problem-solving and encourages seeking additional resources for assistance.
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Im getting really frustrated I've figured a way to get the right answer for a lot of two dimensional motion problems but i cannnott figure out what formulas to use when o use them can anyone give me a list of formulas used to solve these types of problems

another question is Why do two horizontal projectiles dropped from the same height at the same time hit the ground at the same time even if their horizontal velocities are different

can sopmeone pleasee help
An athlete in the Olympics throws ashot put. The shot put is in the air for 1.89 seconds and lands 6.7 meters away horizontally. Calculate the intial vertical and horizontal components of the shot puts angular velocity. (horizontal velocity = Vi (cos 0), initialy veritcal = Vi(sin 0)
i have no idea where to start in this one but

A golf ball lands 123.0 m horizontally away from its position after being stuck. If the ball has an angular velocity of 40.0 m./s and is in the air a total of 6.0 seconds calculate the angle at which the ball was launched

please i have no idea people won't answer cause i can't show work but i don't know what to dooooo pleaseeee somone help me
 
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