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 Kinematics and Dynamics Kinematics and Dynamics Physics Help Forum Jun 3rd 2019, 01:03 AM #1 Junior Member   Join Date: Jun 2019 Posts: 2 Projectile motion: Missile over a hill A missile is to be launched from a point P, 500m from the peak of a hill of height 2000m into enemy territory. If the missile is to just pass over the hill and strike a target 1200m from P, what is the velocity at which the missile should be launched, and the angle of launch?   Jun 4th 2019, 10:39 AM   #2
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 Originally Posted by Leonson A missile is to be launched from a point P, 500m from the peak of a hill of height 2000m into enemy territory. If the missile is to just pass over the hill and strike a target 1200m from P, what is the velocity at which the missile should be launched, and the angle of launch?
$x = v_0 \cos{\theta} \cdot t \implies t = \dfrac{x}{v_0 \cos{\theta}}$

$y = v_0 \sin{\theta} \cdot t - \dfrac{g}{2}t^2$

eliminating the parameter of time yields the equation

$\color{red}{y = x\tan{\theta} - \dfrac{gx^2}{2v_0^2\cos^2{\theta}}}$

using position coordinates $(x,y)$, in the general quadratic $y=ax^2+bx+c$

$P=(0,0)$, $(500,2000)$, and $(1200,0)$

$0 = a\cdot 0^2 + b \cdot 0 + c \implies c = 0$

$2000 = a \cdot 500^2 + b \cdot 500 \implies 500a+b=4$

$0 = a \cdot 1200^2 + b \cdot 1200 \implies 1200a + b = 0$

solving the system of equations yields

$\color{red}{y = -\dfrac{1}{175}x^2 + \dfrac{48}{7}x}$

equating the linear coefficient:

$\tan{\theta} = \dfrac{48}{7} \implies \theta = \tan^{-1}\left(\dfrac{48}{7}\right) \text{ and } \cos{\theta} = \dfrac{7}{\sqrt{48^2+7^2}}$

equating the quadratic coefficient:

$\dfrac{g}{2v_0^2 \cos^2{\theta}} = \dfrac{1}{175}$

you can solve for the magnitude of $v_0$   Jun 4th 2019, 06:50 PM #3 Junior Member   Join Date: Jun 2019 Posts: 2 Thank you for replying! Sorry I didn't include my attempt along with the post😔  Tags hill, missile, motion, projectile, wall Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post ficku1 Kinematics and Dynamics 5 Sep 27th 2017 06:18 AM SMA777 Kinematics and Dynamics 3 Oct 10th 2011 11:24 AM Quacky Kinematics and Dynamics 2 Oct 21st 2010 10:45 AM jsu03 Kinematics and Dynamics 1 Sep 27th 2009 06:46 PM symstar Kinematics and Dynamics 2 Sep 18th 2008 11:45 AM