VA HN 31 (101) Curves by X C Secure I www.webassign net/web Student/Assignment-R

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VA HN 31 (101) Curves by X C Secure I www.webassign net/web Student/Assignment-Responses/last?dep 5423614 https -2.9 points scalceM0 10.1 CM8.nwa My Notes Ask Your Teacher If a projectile is hired with an initial velocity of vo meters per second at an angle a above the horizontal and air resistance is assumed to be negligible, then its position atter t seconds is given by the parametric equations where g Is the acceleratlon due to gravity (9.8 m/s Round your answers to the nearest whole number (a) If a gun is fired with or 300 and vo 300 rrl/s. When will the bullet hit the ground? How far from the gun vill it hit the ground? Vihat is the maximum height reached by the bullet? (b) rind the equation of the parabolic path by eliminating the parameter. Sub Assign Save Assig ent Frogress lity Assign WebAssign8 408 1997-2017 Advenced Instruci Systems Inc. Al rights reserved 22 AM Search the web and Window

Explanation / Answer

Given the parametric equations
x = (vo cos )t --------(i)
y = (vo sin )t 1/2gt^2 -----(ii)

a)

To find the time it takes for the bullet to hit the ground we are only concerned with the equation that gives us height presumably
y = (vo sin )t 1/2gt^2. Since this is a projectile motion, therfore the total height displacement is 0 (i,e, y=0)

therefore our equation becomes

0 = (vo sin )t 1/2gt^2

0 = {(vo sin ) 1/2gt} t => t=0 or (vo sin ) 1/2gt) =0 =>t=0 or t=2vo sin /g --------(1)

We have v0 =800 and = 30o

substitude in (1)

t=0 or t= 81.63

we are not concerned where the bullet started t = 0

t = 81.63 sec

II)

gives us the horizontal displacement it travels and plugging in 81.63  seconds for the time of flight gives us

x = (vo cos )t =800 cos(30) * 81.63 = 56554.92 m

III) To find the max height divide total flight time by 2

Tmax = 81.63 / 2 = 40.815

plugging the time in y = (v sin )t 1/2gt^2 = 800 sin(30) * 40.815 - 1/2 * 9.8 * (40.815)^2 = 8163.265 m

b)

From (1)

x = (vo cos )t => t = x /(vo cos )

Substiute in (2)

y = (vo sin ) x /(vo cos ) 1/2g(x /(vo cos ))^2 = tan - g x2 / (2(vo cos )^2 )

y =  tan - g x2 / (2(vo cos )^2 )

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