We appreciate your visit to If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second its height h after t. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
The toy rocket, launched with an initial velocity of 128 feet per second, will take 4 seconds to return to the ground. We solved this by using the given height-time equation and setting the height to zero to represent landing.
Explanation:
The subject of this question is Physics, specifically projectile motion. To determine how long it will take for the rocket to return to the ground, we need to find when h(t) is equal to zero, which will be when the toy rocket has landed. This is a quadratic equation in the form of at² + bt + c = 0. The coefficients are a = -16 (which represents half the acceleration due to gravity in ft/s²), b = 128 (the initial velocity in ft/s), and c = 0 (the initial height). To find time when the rocket lands, we need to solve for t in the quadratic equation which is given as t = -b/2a. Inserting the givens, we get t = -128 / (2*-16). So, the answer will be t = 4 seconds. Therefore, the toy rocket will take 4 seconds to hit the ground after it was launched.
Learn more about Projectile motion here:
https://brainly.com/question/29545516
#SPJ11
Thanks for taking the time to read If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second its height h after t. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
Answer:
t = 2.82 seconds is the time the rocket launches and returns back to Earth.
Step-by-step explanation:
h(t)= -16t² +128t is telling us the height (h) of the rocket as a function of time (t). It is a quadratic equation and will result in a parabola that starts and stops at (0,0), since it is launched vertically and air resistance (and wind, we assume) is neglected.
We want the time, t, such that h(t) is 0. It has reached ground again.
h(t)= -16t² +128t
0 = -16t² +128t Find t such that h(t) is zero.
-16t² +128t = 0
-16t(t² - 8) = 0
t² - 8 = 0 t = [tex]\sqrt{8}[/tex], or 2.82 sec
and -16t = 0 t = 0 sec
t is either 0 or 2.82
Time of zero means the rocket hasn't launched, so we can disregard that value of t.
t = 2.82 seconds is the time the rocket launches and returns back to Earth. Watch out Musk and Bezos.
