The height in feet of a rocket after t seconds is given by h(t) = 160t - 16t2.
Find the maximum height the rocket attains:
After how many seconds does it reach this height?
by now you know about parabolas.
h(t) = 160t - 16t^2
the vertex of a parabola is at t = -b/2a, which here is
t = 160/32 = 5
So, at t=5, h(t) = 400
Well, to find the maximum height of the rocket, we need to find the vertex of the parabolic function h(t) = 160t - 16t^2. The vertex of a parabola is at the point (h, t) where h is the maximum height and t is the time it takes to reach that height.
Now, the t-coordinate of the vertex can be found using the formula t = -b / (2a), where a and b are the coefficients of the t^2 and t terms, respectively. In this case, a = -16 and b = 160.
Plugging in the values, we get t = -160 / (2*(-16)), which simplifies to t = -160 / -32. And if we simplify it further, we get t = 5.
So, after 5 seconds, the rocket reaches its maximum height.
Now let's find the maximum height. We can substitute the value of t back into the equation h(t) = 160t - 16t^2 to find h.
h(5) = 160(5) - 16(5)^2
= 800 - 16(25)
= 800 - 400
= 400.
So, the maximum height the rocket attains is 400 feet after 5 seconds.
And remember, even though the rocket is at its highest point for just a moment, it's still great at reaching for the stars... or at least the maximum height it can reach!
To find the maximum height the rocket attains, we need to determine the vertex of the parabolic function h(t) = 160t - 16t^2.
The vertex of a parabola in standard form, y = ax^2 + bx + c, can be found using the formula x = -b / (2a).
In this case, a = -16 and b = 160. Plugging these values into the formula, we have:
t = -160 / (2(-16))
t = -160 / (-32)
t = 5
Therefore, the rocket reaches its maximum height after 5 seconds.
To find the maximum height, we substitute this value of t back into the equation:
h(5) = 160(5) - 16(5)^2
h(5) = 800 - 16(25)
h(5) = 800 - 400
h(5) = 400
Hence, the maximum height the rocket attains is 400 feet. It reaches this height after 5 seconds.
To find the maximum height attained by the rocket, we need to determine the vertex of the parabolic function h(t) = 160t - 16t^2.
The vertex of a parabola with equation h(t) = at^2 + bt + c is given by the formula t = -b / (2a), where a, b, and c are the coefficients of the quadratic function.
In this case, a = -16 and b = 160. Plugging these values into the formula, we get:
t = -160 / (2 * -16)
= -160 / (-32)
= 5
So, the rocket reaches its maximum height after 5 seconds.
To find the maximum height, substitute the value of t = 5 into the function h(t) = 160t - 16t^2:
h(5) = 160 * 5 - 16 * 5^2
= 800 - 16 * 25
= 800 - 400
= 400 feet
Therefore, the maximum height attained by the rocket is 400 feet.