SOLUTION: A projectile is fired at an inclination of 45 degrees to the horizontal, with a muzzle velocity of 100 feet per second. The height H of the projectile is modeled by {{{ H(x) =

Question 1011428: A projectile is fired at an inclination of 45 degrees to the horizontal, with a muzzle velocity of 100 feet per second.
The height H of the projectile is modeled by

Where x is the horizontal distance of the projectile from the firing point.
(A) At what horizontal distance from the firing point is the height of the projectile a maximum?
(B) Find the maximum height of the projectile.
(C) At what horizontal distance from the firing point will the projectile strike the ground?
(D) Using a graphing utility, graph the function H,
0(is equal to or less than) x (is equal to or less than) 350
(E) Using the graphing utility to verify the results obtained in parts B and C
(F) when the height of the projectile is 50 feet above the ground, how far has it traveled horizontally?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A projectile is fired at an inclination of 45 degrees to the horizontal, with a muzzle velocity of 100 feet per second.
The height H of the projectile is modeled by

Where x is the horizontal distance of the projectile from the firing point.
(A) At what horizontal distance from the firing point is the height of the
projectile a maximum?
This is quadratic equation, the max will occur at the axis of symmetry; x=-b(2a)
Find a: -32/100^2 = .0064, b = 1
x =
x = +156.25 ft
:
(B) Find the maximum height of the projectile.
x = 156.25

H(x) = 78.125 ft is the max ht
:
(C) At what horizontal distance from the firing point will the projectile strike the ground?
It will be twice the axis of symmetry
x = 2(156.25)
x = 312.5 ft from the origin when it hits the ground
:
(D) Using a graphing utility, graph the function H,
0(is equal to or less than) x (is equal to or less than) 350
Should look like this

(E) Using the graphing utility to verify the results obtained in parts B and C
(F) when the height of the projectile is 50 feet above the ground, how far has it traveled horizontally?
h = 50
= 50

Solve this with the quadratic formula; a=-.0032, b=1, c=-50
Two solutions
x = 62.5 ft on the way up
and
x = 250 ft on the way down
(Green line on the graph is 50')

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