How to find vertical comp. of velcocity?

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To find the vertical component of initial velocity for a non-horizontal projectile when only the initial horizontal velocity and total distance are provided, first calculate the time of flight using the horizontal speed and distance. Once the time is determined, use kinematic equations to find the necessary vertical speed that allows the object to ascend and descend within that time frame. This approach does not require an angle, as the horizontal motion dictates the time of the projectile's flight. Understanding the relationship between horizontal and vertical motion is crucial in solving this problem. The method effectively combines horizontal distance with vertical motion principles to derive the vertical component of velocity.
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If, only the initial velocity in x direction is given and the total distance "S" is given for a non horizontal projectile, how do we find the y (vertical) component of initial velocity? No angle given?
 
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If you know the horizontal speed and distance you know the time.
You can then work out how fast an object must be thrown vertically to take this time to go up and land again.
 

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