A model rocket is launched from the deck in Jim's backyard and the path followed by the rocket can be modeled by the relation
h=-5t^2 +100t +15,
where h, in metres, is the height that the model rocket reaches after t seconds.
What is the height of the deck?
What is the maximum height reached by the rocket?
To find the height of the deck, we need to determine the value of h when t is equal to 0.
Given that h = -5t^2 + 100t + 15, when t = 0:
h = -5(0)^2 + 100(0) + 15
h = 0 + 0 + 15
h = 15
Therefore, the height of the deck is 15 meters.
To find the maximum height reached by the rocket, we need to determine the vertex of the quadratic equation h = -5t^2 + 100t + 15. The vertex formula can be used to find this:
t_vertex = -b / (2a)
where a = -5 and b = 100.
Substituting the values, we get:
t_vertex = -100 / (2(-5))
t_vertex = -100 / (-10)
t_vertex = 10
To find the corresponding height at the vertex, we substitute t = 10 into the equation:
h = -5(10)^2 + 100(10) + 15
h = -5(100) + 1000 + 15
h = -500 + 1000 + 15
h = 515
Therefore, the maximum height reached by the rocket is 515 meters.
To find the height of the deck, we need to determine the value of h when t = 0.
Substituting t = 0 into the equation h = -5t^2 + 100t + 15:
h = -5(0)^2 + 100(0) + 15
h = 0 + 0 + 15
h = 15
Therefore, the height of the deck is 15 meters.
To find the maximum height reached by the rocket, we need to find the vertex of the quadratic equation h = -5t^2 + 100t + 15.
The vertex of a quadratic equation in the form h = at^2 + bt + c is given by the formula t = -b/2a, which gives the x-coordinate of the vertex. To find the y-coordinate, we substitute the x-coordinate back into the equation.
In this case, a = -5, b = 100, and c = 15.
t = -b/2a
t = -100/(2*(-5))
t = -100/(-10)
t = 10
Substituting t = 10 into the equation h = -5t^2 + 100t + 15:
h = -5(10)^2 + 100(10) + 15
h = -5(100) + 1000 + 15
h = -500 + 1000 + 15
h = 515
Therefore, the maximum height reached by the rocket is 515 meters.
when t=0, the rocket is on the deck, right?
so, what is h(0)?
the max height is reached when t = -b/2a = 10
so, what is h(10)