If a projectile is fired straight upward from the ground with an initial speed of 128 feet per second, then its height h in feet aftert seconds is given by the function h(t) = -16t + 128t. Find the maximum height of the projectile.

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Louis Page · Accepted Answer

Given height function h(t)=−16t2+128tWe have to find the maximum height of the projectile.∴h(t)=−16t2+128tSo, h′(t)=−16(2t)+128⇒h′(t)=−32t+128To get the critical point, we put h′(t)=0 and solve for &quot;t&quot;.∴h′(t)=0⇒−32t+128=0⇒−32t=−128⇒t=−128−32⇒t=4So, the critical point is t=4.Now, ht)=ddt(h′(t))=ddt(−32t+128)=−32So, ht)=−32at t=4,h4)=−32&amp;lt;0So, by second derivativetest, h(t) has maximum value at t=4∴h(4)=−16×42+128×4=−256+512=256Henca, the maximum height of the projective is 256 feet.

Mary Goodson · Accepted Answer

h(t)=−16t2+64t complete the square h(t)=−16(t2−4t+4)+64 h(t)=−16(t−2)2+64 This is an equation of a parabola that opens upward with vertex at (2,64) maximum height of the projectile =64 ft (2 sec after it is fired)

user_27qwe · Accepted Answer

For this case we have the following function: Deriving the function we have: h&#039;(t)=-32t + 128 Equaling zero we have: -32t + 128 = 0 We clear the time: t=12832 t = 4 Substituting in the height equation: h(4)=−16∗(4)2+128∗(4) h(4) = 256 feet Answer: The maximum height is: h (4) = 256 feet

Mr Solver · Accepted Answer

The given function is:h(t)=−16t+128tTo find the vertex, we first need to convert the function to vertex form. The vertex form of a quadratic function is given by:f(t)=a(t−h)2+kwhere (h,k) represents the coordinates of the vertex.Let&#039;s begin by factoring out the common factor of t from the equation:h(t)=t(−16+128)Simplifying further:h(t)=112tNow, let&#039;s rewrite the equation by completing the square. We can do this by adding and subtracting the square of half the coefficient of t:h(t)=112(t−0)2Comparing this with the vertex form equation, we can see that h=0 and k=0. Therefore, the vertex of the parabola is (0,0).Since the projectile is fired straight upward, the maximum height is attained at the vertex of the parabolic function. In this case, the maximum height is 0 feet.Hence, the maximum height of the projectile is 0 feet.

madeleinejames20 · Accepted Answer

To find the vertex, we can use the formula h=−b2a, where a is the coefficient of the squared term and b is the coefficient of the linear term.In this case, a=−16 and b=128. Substituting these values into the formula, we get:h=−1282(−16)=−128−32=4Therefore, the t-coordinate of the vertex is t=4. To find the corresponding height, we substitute this value back into the equation:h(4)=−16(4)2+128(4)Simplifying this expression gives us:h(4)=−16(16)+128(4)=−256+512=256The maximum height of the projectile is 256 feet.

If a projectile is fired straight upward from the ground

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