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Lilit [14]
3 years ago
5

A rocket is launched straight up from the ground, with an initial velocity of 224 feet per second. The equation for the height o

f the rocket at time t is given by:
h=-16t^2+224t

(Use quadratic equation)

A.) Find the time when the rocket reaches 720 feet.


B.) Find the time when the rocket completes its trajectory and hits the ground.

Mathematics
2 answers:
JulijaS [17]3 years ago
6 0

A.) The rocket reaches 720 feet in 5 seconds and 9 seconds.

B.) The rocket completes its trajectory and hits the ground in 14 seconds

<h3>Further explanation</h3>

A quadratic equation has the following general form:

ax^2 + bx + c = 0

The formula to solve this equation is :

\large {\boxed {x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} } }

Let's try to solve the problem now.

<h2>Question A:</h2>

Given :

h = -16 t^2 + 224t

The rocket reaches 720 feet → h = 720 feet

720 = -16 t^2 + 224t

16 t^2 - 224t + 720 = 0

16 (t^2 - 14t + 45 = 0)

t^2 - 14t + 45 = 0

t^2 - 9t - 5t + 45 = 0

t(t - 9) - 5(t - 9) = 0

(t - 5)(t - 9) = 0

t = 5 ~ or ~ t = 9

The rocket reaches 720 feet in 5 seconds and 9 seconds.

<h2>Question B:</h2>

The rocket hits the ground → h = 0 feet

0 = -16 t^2 + 224t

16 (t^2 - 14t ) = 0

t^2 - 14t = 0

t( t - 14 ) = 0

t = 0 ~ or ~ t = 14

The rocket completes its trajectory and hits the ground in 14 seconds

<h3>Learn more</h3>
  • method for solving a quadratic equation : brainly.com/question/10278062
  • solution(s) to the equation : brainly.com/question/4372455
  • best way to solve quadratic equation : brainly.com/question/9438071

<h3>Answer details</h3>

Grade: College

Subject: Mathematics

Chapter: Quadratic Equation

Keywords: Quadratic , Equation , Formula , Rocket , Maximum , Minimum , Time , Trajectory , Ground

serious [3.7K]3 years ago
3 0
We can model the equation of the height of the rocket as ∩-shape curve as shown below

Part A: 

The time when the height is 720 feet

720 = -16 t^{2}+224t, rearrange to make one side is zero
16 t^{2}-224t+720=0, divide each term by 16
t^{2} -14t+45 =0, factorise to give
(t-9)(t-5)=0
t=9 and t=5

So the rocket reaches the height of 720 feet twice; when t=5 and t=9

Part B:

We will need to find the values of t when the rocket on the ground. The first value of t will be zero as this will be when t=0. We can find the other value of t by equating the function by 0

0=-16 t^{2}+224t
0=-16t(t-14)
-16t=0 and t-14=0
t=0 and t=14

So the time interval when the rocket was launched and when it hits the ground is 14-0 = 14 seconds




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