A projectile is fired from a cliff 200 feet above water at an inclination of 45

Question

A projectile is fired from a cliff 200 feet above water at an inclination of 45 degrees to the horizontal, with a muzzle velocity of 45 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 face of the cliff. Use this information to answer the following.

A) At what horizontal distance from the face of the cliff is the height of the projectile at a maximum? x=____ feet
B) Find the maximum height of the projectile. h=___ feet.

C)At what horizontal distance from the face of the cliff will the projectile strike the water? x=___ feet.

E) When the height of the projectile is 100 feet above the water, how far is it from the cliff? x=___ feet

Explanation / Answer

h(x) = -32x^2 / 2025 + x + 200

a) at x = -1 / 2 ( -32/2025)

x = 31.64 feet the height of projectile is maximum

b) maximum height is  -32(31.64)^2 / 2025 + 31.64 + 200

h = 215.82 feet

c) strike the water means height = 0

setting the equation to 0

-32x^2 / 2025 + x + 200 = 0

x = 148.51

at x = 148.51 feet from the face cliff the projectile will strike the water

d) setting height h = 100

-32x^2 / 2025 + x + 200 = 100

x = 117 feet

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.