If the flight of a rocket can be modelled by the function h=-4.9t^2+49t+2.5. Where h is height in meters and t is time in seconds. How long was the rocket above 100m?
I know that you have to find the two times when the rocket hits 100m. And then subtract them. But how do you find the time when it hits 100m?
100=-4.9t^2+49t+2.5. How do you find the two t?
it's sad that it's 2021 and still no reply.
I know you can use the formula. But I'd there another way?
To find the time when the rocket reaches a height of 100 meters, you need to solve the following equation:
-4.9t^2 + 49t + 2.5 = 100
First, rearrange the equation to bring all terms to one side:
-4.9t^2 + 49t + 2.5 - 100 = 0
Now, you have a quadratic equation in the form of at^2 + bt + c = 0, with:
a = -4.9
b = 49
c = 2.5 - 100 = -97.5
To solve quadratic equations, you can use either factoring, completing the square, or the quadratic formula. In this case, we'll use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values from our equation:
t = (-49 ± √(49^2 - 4 * (-4.9) * (-97.5))) / (2 * (-4.9))
Simplifying further:
t = (-49 ± √(2401 + 19392)) / (-9.8)
t = (-49 ± √(21793)) / (-9.8)
Now, you can calculate two possible solutions for t by taking the positive and negative square roots of 21793:
t1 = (-49 + √(21793)) / (-9.8)
t2 = (-49 - √(21793)) / (-9.8)
Simply calculate the values within the square root, and then compute each t value separately. These values will give you the times when the rocket reaches a height of 100 meters.