Question
A football quarterback is moving straight backward at a speed of 2.00 m/s when he throws a pass to a player 18.0 m straight downfield. The ball is thrown at an angle of $25.0^\circ$ relative to the ground and is caught at the same height as it is released. What is the initial velocity of the ball relative to the quarterback?

$17.0 \textrm{ m/s, } 22.2^\circ \textrm{ above horizontal}$

OpenStax College Physics, Chapter 3, Problem 56 (Problems & Exercises)

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Video Transcript
Hi Blue, the 18m range is used in the very beginning of the solution to find $v_o$, the initial speed of the ball with respect to the ground. The 18m was used in the range formula to find $v_0$ at 1:53. The 18m range isn't used any more after that. At 7:43 what you're seeing in red is the resultant velocity, not the displacement. This resultant is the vector sum of the velocity of the ball with respect to ground (which we know by 1:53 in the video since the question tells us the launch angle), plus the velocity of the ground with respect to the quarterback (which is worded slightly confusingly - not quarterback with respect to the ground). We need to figure out the red vector to answer the question of the velocity of the ball with respect to the quarterback.