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A rocket is shot straight into the air at an initial velocity of 70 feet/second.
The height of the rocket after t seconds is represented by the formula
h = 70t - 5tº. What is the maximum height the rocket reaches?
235 feet
265 feet
215 feet
245 feet

Sagot :

JeanaShupp

Answer: 245 feet

Step-by-step explanation:

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

[tex]h=70t-5t^2[/tex]

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

Put

[tex]\dfrac{dh}{dt}=0\\\\\Rightarrow\ 70-10t=0\\\\\Rightarrow\ t=\dfrac{70}{10}=7[/tex]

Also, [tex]\dfrac{d^2h}{dt^2}=-10<0[/tex] i.e. height is maximum at t=7.

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

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

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