The height above ground level in metres of a missile lanunched vertically, is given by h(t)=-16t^3+100t. at what time is the missile 50m above the ground level? [t is time in seconds]
just solve
-16t^3+100t = 50
in the usual way
Although, I think you want the height in feet, since in metric units, g/2 = -4.9, not -16
Result
To find the time when the missile is 50 meters above the ground level, we need to set the height function h(t) equal to 50 and solve for t.
The height function is given as h(t) = -16t^3 + 100t.
So we have the equation:
-16t^3 + 100t = 50
To solve this equation for t, we need to rearrange it and then use some algebraic techniques to simplify it. Here's how you can do it:
1. Subtract 50 from both sides of the equation:
-16t^3 + 100t - 50 = 0
2. Now we have a cubic equation in standard form. To solve this, we can either use numerical methods or factoring if possible. In this case, let's factor out the common factor of 2:
2(-8t^3 + 50t - 25) = 0
3. We are left with a quadratic expression inside the parentheses:
-8t^3 + 50t - 25 = 0
4. Unfortunately, factoring this equation further is not straightforward. So, we can use numerical methods, such as graphing the equation or using a calculator, to find the approximate value of t when the height is 50 meters.
Alternatively, you can use numerical solving tools, such as online equation solvers or graphing calculators, which can provide a more accurate solution.
By plugging in the equation -8t^3 + 50t - 25 = 0 into an equation solver, you can find the value of t when the height is 50 meters.