Question

The height of a fireworks rocket in meters can be approximated by h= -5t^2+30t, where h is the height in meters and t is the time in seconds. Find the time it takes the rocket to reach the ground after it has been launched

Answer 1

Answer:

It takes 6 seconds to the rocket to reach the ground after it has been launched

Step-by-step explanation:

The height of a fireworks rocket in meters can be approximated by :

h = -5t² + 30t, where h is the height in meters and t is the time in seconds

Now, we need to find the time it takes the rocket to reach the ground after it has been launched

So, When it touches the ground height will be 0

⇒ h = 0

⇒ 0 = -5t² + 30t

⇒ t² - 6t = 0

⇒ t(t - 6) = 0

Now, since the rocket is launched from above the ground ⇒ t ≠ 0

⇒ t - 6 = 0

⇒ t = 6

Hence, It takes 6 seconds to the rocket to reach the ground after it has been launched

Answer 2

It takes 45 seconds. the easiest way to do these is to use a graphic calculator and replace the variables with x and y, for example, this equation would become -5x^2+30x, and if you don't have access to a graphing calculator, you can always use desmos online.