Mathematics: Nasa launches a rocket at t = 0 seconds. its height, in meters above sea-level, as a function of time is given by h ( t ) = − 4.9t^2 + 202t + 318 . assuming that the rocket will splash down into the ocean, at what time does splashdown occur? the rocket splashes down . how high above sea-level does the rocket get at its peak? the rocket peaks above sea-level

I had 61.09090909 repeating as a answer, you can round it, but if you divide 168 by 11 because that is the total amount of people then that gives a decimal place and that doesn t make sense. But I may be right. So best of luck. If I get you wrong then I am truly sorryStep-by-step explanation:...

Nasa launches a rocket at t = 0 seconds. its height,

Ответ:

sindy35111

10.03.2022

Mathematics

The rocket splashes down after 43 seconds.

The rocket peaks at 2400. meters above sea-level.

Step-by-step explanation: For the time taken before the splash

Step 1

We realise that the rocket will hit the ground when our function h(t)=0 , i.e -4.9t^2+202t+318=0.

Step 2

Use the quadratic formula to solve for the time. For the general quadratic equation at^2+bt+c=0 , the general solution to the equation is

$t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} .$

In our case, the quadratic equation h(t)=-4.9t^2+202t+318=0 has a solution

$t=\frac{-202\pm\sqrt{202^2-4((-4.9)(318))}}{2(-4.9)} \\t=-1.52,t=42.74.$

Step 3

In this step we pick the value of that makes physical sense. Since the NASA team launced the rocket at t=0 , the rocket reaches the bottom when t=42.74 . This can be rounded up to seconds.

For the maximum height of the rocket above sea level

Step 1

The first step is to realist that since the coefficient of the quadratic term is negative, the graph of this function will face downwards. From this we can gather that the maximum value of this function occurs at the vertex.

Step 2

In this step we calculate the t coordinate of the of the vertex of this function. For any quadratic equation h(t)=at^2+bt+c , the vertex occurs when ,