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gtnhenbr [62]
2 years ago
13

A model rocket is launched from the ground with an initial velocity of 120 feet per second. The height of an object h, in feet,

after t seconds, with initial velocity v0 and initial height h0 is given by h(t)=−16t2+v0t+h0 . What is the approximate maximum height the rocket reaches?
Mathematics
2 answers:
hichkok12 [17]2 years ago
8 0

Answer:

The rocket will reach a maximum height of 225 feet from the ground in 3.75 seconds.      

Step-by-step explanation:

We are given the following information in the question:

Initial velocity = v_0 = 120 feet per second

Initial heigth = h_0

h(t) = -16t^2 + v_0t + h_0

h(t) is a function of t that gives height of the rocket at time t, initial velocity v_0. intial height h_0.

Differentiating h(t) with respect to t, we get:

\displaysttyle\frac{d(h(t))}{dt} = -32t + v_0

Equating the first derivative to zero,

-32t + v_0 = 0\\-32t = -120 \\t = \displaystyle\frac{120}{32} = 3.75

Again differentiating, h(t) with respect to t,

\displaysttyle\frac{d^2(h(t))}{dt^2} = -32 < 0

Hence, h(t) will have a local maxima by double derivative test.

Maximum height attained by rocket =

h(\displaystyle\frac{120}{32}) = -16\times \frac{120}{32}\times \frac{120}{32} + 120\times \frac{120}{32} + 0 = 225 \text{ feet}

Hence, the rocket will reach a maximum height of 225 feet from the ground in 3.75 seconds.

Talja [164]2 years ago
6 0
567 is the height it reaches
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