A ball is thrown from an initial height of 1 meter with an initial upward velocity of 9 m/s. The ball's height h (in meters) after t seconds is given by the following
h=1+9t-5t^2
Find all the values of the t for which the ball's height is 4 meters.
ergf
Well, to find the values of t for which the ball's height is 4 meters, we can simply substitute h = 4 into the equation and solve for t. Let's give it a try:
4 = 1 + 9t - 5t^2
Hmm, this equation reminds me of my math teacher trying to juggle flaming bowling pins. Let's rearrange the terms and see if we can solve it:
5t^2 - 9t + 3 = 0
Now, we can either use the quadratic formula or try to factor this expression. I prefer the former, just to be fair to all the formulas out there:
t = (-b ± √(b^2 - 4ac)) / 2a
For our equation, a = 5, b = -9, and c = 3. We plug these values into the formula, and voila! We get:
t = (9 ± √((-9)^2 - 4 * 5 * 3)) / (2 * 5)
Simplifying further, we have:
t = (9 ± √(81 - 60)) / 10
t = (9 ± √21) / 10
So, the values of t for which the ball's height is 4 meters are approximately:
t ≈ (9 + √21) / 10 and t ≈ (9 - √21) / 10
Well, that's a few seconds of calculating for just a single height measurement. I hope the ball doesn't stop at 4 meters too often, or else this math problem would be quite exhausting!
To find the values of t for which the ball's height is 4 meters, we need to solve the equation h = 4.
The given equation is h = 1 + 9t - 5t^2. Plugging in h = 4, we get 4 = 1 + 9t - 5t^2.
Rearranging the equation, we get 5t^2 - 9t + 3 = 0.
Now we can solve this quadratic equation to find the values of t.
We can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 5, b = -9, and c = 3. Plugging these values into the formula, we get:
t = (-(-9) ± √((-9)^2 - 4 * 5 * 3)) / (2 * 5)
t = (9 ± √(81 - 60)) / 10
t = (9 ± √21) / 10
So the values of t for which the ball's height is 4 meters are (9 + √21) / 10 and (9 - √21) / 10.
two values ... going up and coming down
4 = 1 + 9 t - 5 t^2 ... 5 t^2 - 9 t + 3 = 0
use quadratic formula to find t