Calculating Vo for a Basketball Shot at 40 Deg Angle

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To calculate the initial velocity (Vo) required for a basketball player to make a shot at a 40-degree angle, the player must consider the distance to the basket and the height difference. The equations used involve time (t) and the vertical motion of the ball, factoring in the player's height and the basket's height. By substituting the expression for time into the vertical motion equation, Vo can be isolated. The calculations involve trigonometric functions and kinematic equations. Ultimately, this method allows for determining the necessary initial speed for a successful shot.
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A 2.00m tall basket ball player is standing on the floor 10m from the basket. If he shoots the ball at 40 degrees angle with the horizontal, at what initial speed must he throw the basketball so that i goes through the hoop? The height of the basket is 3.05m.

Here how do i calculate for Vo?
i get t=10/(VoCOS40) and 1.05=(VoSIN40)t - 4.9t^2
 
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Substitute that t into your y distance equation and do some manipulation so that V0 is the subject.
 

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