Solve.
-A projectile is fired from a cliff 400 feet above the water at an inclination of $45 ^ { \circ }$ to the horizontal, with an initial velocity of 290 feet per second. The height $h$ of the projectile above the water is given by $h ( x ) = \frac { - 32 x ^ { 2 } } { ( 290 ) ^ { 2 } } + x + 400$, where $x$ is the horizontal distance of the projectile from the base of the cliff. Find the maximum height of the projectile.
A) $1057.03 \mathrm { ft }$
B) $657.03 \mathrm { ft }$
C) $2371.09 \mathrm { ft }$
D) $1314.06 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The maximum height of a projectile in a parabolic motion can be found by completing the square or using the vertex formula for a parabola. The given equation is in the form $h(x) = ax^2 + bx + c$, where $a = \frac{-32}{(290)^2}$, $b = 1$, and $c = 400$. The vertex of this parabola, which gives the maximum height when $a < 0$, occurs at $x = -\frac{b}{2a}$. Substituting the given values, we find the maximum height by evaluating $h(x)$ at this $x$ value. The calculation leads to the maximum height being approximately $1057.03$ feet, which corresponds to choice A.

Solve -A Projectile Is Fired from a Cliff 400 Feet 45∘45 ^ { \circ }45∘

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-A Projectile Is Fired from a Cliff 400 Feet $45 ^ { \circ }$