June 12th, 2019, 01:37 AM  #1 
Member Joined: Feb 2018 From: Iran Posts: 52 Thanks: 3  Projectile motion
How would time of flight, the range and the maximum height of an object exhibiting the projectile motion change if A) only the vertical component of its initial velocity is increased, B) only the horizontal component of its initial velocity is increased? Last edited by skipjack; June 12th, 2019 at 01:54 AM. 
June 12th, 2019, 05:02 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600 
$y = y_0 + v_{0y} \cdot t  \dfrac{1}{2}gt^2$ maximum height occurs when $\dfrac{dy}{dt} = 0$ $\dfrac{dy}{dt} = v_{0y}  gt = 0 \implies t = \dfrac{v_{0y}}{g}$ Increasing $v_{0y}$ results in a greater time to reach maximum height, hence a higher trajectory and longer overall time of flight which also increases the horizontal range since $\Delta x = v_x \cdot t$ Increasing only $v_x$ increases the horizontal range. 

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