Questions: A model rocket is launched with an initial upward velocity of 151 ft/s. The rocket's height (in feet) after t seconds is given by the following equation: h = 151t - 16t^2 Find all values of t for which the rocket's height is 88 feet. (If there is more than one answer, use the "or" button.) t = [] seconds x ground

A model rocket is launched with an initial upward velocity of 151 ft/s. The rocket's height (in feet) after t seconds is given by the following equation:

h = 151t - 16t^2

Find all values of t for which the rocket's height is 88 feet.
(If there is more than one answer, use the "or" button.)

t = [] seconds

x ground

Transcript text: A model rocket is launched with an initial upward velocity of 151 ft/s. The rocket's height (in feet) after t seconds is given by the following equation: h = 151t - 16t^2 Find all values of t for which the rocket's height is 88 feet. (If there is more than one answer, use the "or" button.) t = [] seconds x ground

Solution

Solution Steps

Step 1: Rearrange the given equation to form a quadratic equation

The equation is rearranged to $-g t^2 + v_0 t - h = 0$, where $g = 16$, $v_0 = 151$, and $h = 88$.

Step 2: Calculate the discriminant

The discriminant is calculated as $v_0^2 + 4gh = 151^2 + 4_-16_-88 = 17169$. Since the discriminant is positive, there are two distinct real solutions for $t$.

Step 3: Solve the quadratic equation

Using the quadratic formula, $t = \frac{-v_0 \pm \sqrt{v_0^2 - 4gh}}{2(-g)}$, we find the solutions for $t$ as 0.62 and 8.81.