an airplane flying horizontally at a speed of 180mi/hr at 400ft drops a package at A. the package has a parachute which deployes at B and allows the package to decend vertically at 6ft/s if it drop is designed so the package reaches the ground after 37 seconds from being released. determine the horizontal distance. neglect air resistance.

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anonymous · Answer

I'm assuming that once under parachute, the package has no horizontal velocity.  With that in hand, the first order of business is to find out how long the package is in free fall.  We know these things: the acceleration of gravity; the total time the package is moving toward the ground (37 seconds); the velocity at which the package descends under parachute (6ft/s);and the total height the package travels (400ft).  The distance the package free falls is given by:$$y _{f}=\frac{ 1 }{ 2 }g t ^{2}$$where yf is the distance the package free falls; g is the acceleration of gravity; and t is time.  The height the package covers under parachute is given by:$$y _{p}=6\left( 37-t \right)$$where yp is the distance travelled under parachute; and t is time.  We know that:$$y _{f}+y _{p}=400ft$$So we can do some substitution to find:$$400=\frac{ 1 }{ 2 }g t ^{2}+6\left( 37-t \right)$$That allows you to find the time in free fall, t. Using that, you can find the horizontal distance traveled using:$$x=v _{x}t$$where x is the horizontal distance traveled; vx is the horizontal velocity; and t is again time.  Pay attention to your units.