Use the formula h= -16t^2+250t to model the height 'h' in feet of a model rocket 't' seconds after it has luanched. Determine when the rocket will reach a height of 900 feet.
honestly giey
To determine when the rocket will reach a height of 900 feet, we can substitute h = 900 into the formula h = -16t^2 + 250t and solve for t.
So, we have:
900 = -16t^2 + 250t
To solve this quadratic equation, we need to rearrange it and set it equal to zero:
-16t^2 + 250t - 900 = 0
Now, we can either factor the equation or use the quadratic formula to find the values of t that satisfy this equation.
Let's use the quadratic formula:
The quadratic formula states that for any quadratic equation in the form of ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / 2a
In our case, a = -16, b = 250, and c = -900. Substituting these values into the quadratic formula, we have:
t = (-250 ± √(250^2 - 4(-16)(-900))) / 2(-16)
Let's simplify this equation:
t = (-250 ± √(62500 - 57600)) / -32
t = (-250 ± √4900) / -32
t = (-250 ± 70) / -32
We have two possible solutions:
1. t = (-250 + 70) / -32
t = -180 / -32
t = 5.625
2. t = (-250 - 70) / -32
t = -320 / -32
t = 10
Therefore, the rocket will reach a height of 900 feet at approximately 5.625 seconds and 10 seconds after it has launched.