anonymous
  • anonymous
GIVEN: A projectile is fired from the bottom of a 240 ft. deep gorge and is visible only when the projectile is above the rim of the gorge. If the projectile is fired with an initial velocity of 175 ft/s, the height of the projectile from ground level after t seconds is given by s(t) = -16t2 + 175t - 240 (a) During what interval can the projectile be seen? (b) What is the maximum height of the projectile?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
for b...you can find the maximum height by taking the derivative, solving for the zeros of the derivative and doing the first derivative test to find the maximum
anonymous
  • anonymous
a) since the projectile can only be seen from above the rim of the gorge, \[-16t^2+175t-240\ge 240\] solve this and take only the positive values of t
anonymous
  • anonymous
^^ if any

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anonymous
  • anonymous
u should find that the maximum is when t=175/32
anonymous
  • anonymous
I calculated a max height of 238.5, but does that mean it would always fall short of the 240 foot height rim of the gorge?
anonymous
  • anonymous
yes
anonymous
  • anonymous
So there is no interval during which the projectile would be visible at ground level, right?
anonymous
  • anonymous
when you solve the equation given for part a greater than 240...it will never exist
anonymous
  • anonymous
b) the maximum height will be at -32t+175=0 that is t=175/32 therefor the maximum height is \[H_\max= v_i+s(175/32)\]
anonymous
  • anonymous
sorry
anonymous
  • anonymous
wait...i just realized that the equation is given from ground level
anonymous
  • anonymous
so the maximum height the is 238.51 above ground level
anonymous
  • anonymous
so part a is written wrong
anonymous
  • anonymous
−16t2+175t−240≥0
anonymous
  • anonymous
you should be solving −16t2+175t−240≥0 for part a
anonymous
  • anonymous
\[H_\max=V_i/t_o+s(t_0), t_0=175/32\]
anonymous
  • anonymous
\[V_i*t_0\]*
anonymous
  • anonymous
I am making so many mistakes :(
anonymous
  • anonymous
for part a you should get t needs to be between 1.6078 and 9.3297
anonymous
  • anonymous
dont worry....i misread the problem at first too
anonymous
  • anonymous
But why isn't the max height then 478.5 (240+238.5), if its 238.5 feet above ground level. How can s(0) be at ground level when its being shot from 240 feet underground? I am so confused.
anonymous
  • anonymous
its not above ground until 1.6078
anonymous
  • anonymous
im guessing that part b is the max height from ground and not from the gorge since the equation given is from the ground

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