Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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.

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.