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KIM [24]
3 years ago
10

A rocket is shot straight into the air at an initial velocity of 70 feet/second.

Mathematics
1 answer:
DanielleElmas [232]3 years ago
3 0

Answer: 245 feet

Step-by-step explanation:

Given: The height of the rocket after t seconds is represented by the formula:

h=70t-5t^2

\dfrac{dh}{dt}=70-10t  [Differentiate both sides w.r.t. t]

Put

\dfrac{dh}{dt}=0\\\\\Rightarrow\ 70-10t=0\\\\\Rightarrow\ t=\dfrac{70}{10}=7

Also, \dfrac{d^2h}{dt^2}=-10 i.e. height is maximum at t=7.

Maximum height = h=70(7)-5(7)^2 = 490 - 245= 245\text{ feet}

Hence, the maximum height the rocket reaches = 245 feet.

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