SOLUTION: A projectile is fired from a cliff 100 feet above the water at an inclination of 45� to the horizontal, with a muzzle velocity of 170 feet per second. The height h of the projecti

Question 471804: A projectile is fired from a cliff 100 feet above the water at an inclination of 45� to the horizontal, with a muzzle velocity of 170 feet per second. The height h of the projectile above the water is given by

where x is the horizontal distance of the projectile from the base of the cliff. How far from the base of the cliff is the height of the projectile a maximum?
A. 225.78 ft
B. 451.56 ft
C. 325.78 ft
D. 777.34 ft

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A projectile is fired from a cliff 100 feet above the water at an inclination of 45� to the horizontal, with a muzzle velocity of 170 feet per second. The height h of the projectile above the water is given by

where x is the horizontal distance of the projectile from the base of the cliff. How far from the base of the cliff is the height of the projectile a maximum?
:
Convert the coefficient of x^2 to a more manageable value
:
= -.001107, so we have
h(x) = -.001107x^2 + x + 100
:
find the axis of symmetry, x = -b/(2a), in this equation a=-.001107, b=1
x =
x = +451.6 ft from the base of the cliff, it will be at max height

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