the height above ground level in meters of a missile launched vertically is given by :
h(t) = -16t^3 + 100t
at what time is the missile 72m above ground level? (t of time in a second)
To find the time when the missile is 72m above ground level, we need to solve the equation h(t) = 72.
Given: h(t) = -16t^3 + 100t
Substituting h(t) with 72, we have:
72 = -16t^3 + 100t
Now, let's solve this equation step-by-step:
1. Rewrite the equation in standard form:
-16t^3 + 100t - 72 = 0
2. Simplify the equation:
-16t^3 + 100t - 72 = -16t^3 + 100t - 72 = -16t^3 + 100t - 72 = -16t^3 + 100t - 72 = -16t^3 + 100t - 72 = 0
3. Factor out common terms:
4(-4t^3 + 25t - 18) = 0
4. Divide both sides by 4:
-4t^3 + 25t - 18 = 0
5. Now, we can solve this equation. We can use numerical methods or the rational root theorem to find the root. In this case, let's use numerical methods or a graphing calculator to solve it.
Using numerical methods or a graphing calculator, we find that the approximate value of t is 1.2 seconds.
Therefore, the missile will be 72m above ground level at approximately 1.2 seconds after launch.
To find the time when the missile is 72 meters above ground level, we need to set the height function h(t) equal to 72 and solve for t. The height function is given as:
h(t) = -16t^3 + 100t
So, we can set up the equation:
-16t^3 + 100t = 72
To solve this equation, we'll follow these steps:
Step 1: Move all terms to one side to set the equation equal to zero:
-16t^3 + 100t - 72 = 0
Step 2: Simplify the equation if possible:
-16t^3 + 100t - 72 = 0
Step 3: Factor out common terms, if possible. This equation cannot be factored since it contains t^3 term.
Step 4: Use numerical methods or approximation techniques to solve the equation. One common numerical method is to use the Newton-Raphson method or a graphing calculator.
Alternatively, we can use a numerical method such as the bisection method or the Newton-Raphson method to solve the equation.
Let's use an online graphing calculator such as Desmos to graph the equation and find the solution graphically.
By graphing the equation -16t^3 + 100t = 72 on Desmos, we can visually determine the value of t when the height is 72 meters above ground level.
HEY typos???
Your equation uses g = 32 FEET /s^2 (so g/2 = 16 not 4.9) not 9.81 m/s^2
and uses t^3 instead of t^2
do physics much?
Do You want 72 feet maybe ?
if so
16 t^2 - 100 t + 72 = 0
solve quadratic
t on the way up = 0.83 second
t on the way down = 5.42 seconds