Questions: A ball is thrown from an initial height of 2 feet with an initial upward velocity of 17 ft/s. The ball's height h (in feet) after t seconds is given by the following:
h = -16t^2 + 17t + 2
Find all values of t for which the ball's height is 6 feet.
(If there is more than one answer, use the "or" button.)
t = (17 ± sqrt(17^2 - 4(-16)(2-6)))/(2(-16)) = (17 ± sqrt(289 + 256))/(-32) = (17 ± sqrt(545))/(-32)
Round your answer(s) to the nearest hundredth.
seconds
Transcript text: A ball is thrown from an initial height of 2 feet with an initial upward velocity of 17 ft/s. The ball's height h (in feet) after t seconds is given by the following:
h = -16t^2 + 17t + 2
Find all values of t for which the ball's height is 6 feet.
(If there is more than one answer, use the "or" button.)
t = \frac{17 \pm \sqrt{17^2 - 4(-16)(2-6)}}{2(-16)} = \frac{17 \pm \sqrt{289 + 256}}{-32} = \frac{17 \pm \sqrt{545}}{-32}
Round your answer(s) to the nearest hundredth.
seconds
Solution
Solution Steps
Step 1: Set the equation equal to 6.
The given equation is h = 2 + 17t - 16t². We are looking for the time(s) when the height (h) is 6 feet. So, we set the equation equal to 6:
6 = 2 + 17t - 16t²
Step 2: Rearrange the equation into standard quadratic form.
Subtract 6 from both sides of the equation to get the equation in standard quadratic form (ax² + bx + c = 0):
0 = -16t² + 17t - 4
Step 3: Solve for _t_ using the quadratic formula.
The quadratic formula is: t = (-b ± √(b² - 4ac)) / 2a
In our equation, a = -16, b = 17, and c = -4. Plug these values into the quadratic formula:
t = (-17 ± √(17² - 4_(-16)_(-4))) / (2 * -16)
t = (-17 ± √(289 - 256)) / -32
t = (-17 ± √33) / -32
Step 4: Calculate the two possible values for _t_.