the height above ground level i
n meters of a missile launched vertically ,is given by h(t)=-16t3+100t .at what time is the missile 72mabove ground level ? (t is time in seconds)
get vertex by complete square method
to use derivatives
I havenot respond!!!! But the question is more complex for me..
Math
Maths
Solution
To find the time at which the missile is 72 meters above ground level, we can plug this height into the equation for h(t) and solve for t.
Given: h(t) = -16t^3 + 100t
We know that at a certain time t, the height is 72 meters: h(t) = 72
So, we substitute h(t) with 72 in the equation:
72 = -16t^3 + 100t
To solve for t, we need to rearrange the equation:
-16t^3 + 100t - 72 = 0
Now, we can use numerical methods like the Newton-Raphson method or the bisection method to approximate the value of t that satisfies the equation. However, since this is a specific problem, we can solve it by factoring.
First, let's factor out a common factor of 8:
8(-2t^3 + 12.5t - 9) = 0
Now, we need to solve the equation -2t^3 + 12.5t - 9 = 0.
To solve this cubic equation, we can use a numerical method or guess values for t and test them until we find the correct solution. In this case, we can use the Rational Root Theorem to determine potential rational solutions.
The Rational Root Theorem states that if a polynomial has a rational root p/q, where p is a factor of the constant term (-9) and q is a factor of the leading coefficient (-2), then p is a factor of the constant term and q is a factor of the leading coefficient.
In this case, the leading coefficient is -2, so q can be either 1 or 2. The constant term is -9, so p can be -1, -3, -9, 1, 3, or 9.
By trying out these potential rational roots and using synthetic division, we find that t = 2 is a solution.
Therefore, the missile is 72 meters above ground level at t = 2 seconds.
just solve for t in
-16t^2 + 100t = 72
This assumes a normal rocket trajectory under constant gravity. Not sure where a cubic function would work.