A model rocket is launched with an initial upward velocity of $70 m / s$ . The rocket's height $h$ (in meters) after $t$ seconds is given by the following.
$h = 70 t - 5 t^{2}$
Find all values of $t$ for which the rocket's height is 35 meters.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
$t = \prod seconds$

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Final Answer: The values of $t$ for which the rocket's height is 35 meters are $0.52$ seconds or $13.48$ seconds.

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Step 1 ：The problem is asking for the time $t$ when the height $h$ of the rocket is 35 meters. This is a quadratic equation problem.

Step 2 ：We can solve it by setting the equation $70 t - 5 t^{2} = 35$ and solving for $t$ .

Step 3 ：We can use the quadratic formula to solve for $t$ , which is $t = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ , where $a = - 5$ , $b = 70$ , and $c = - 35$ .

Step 4 ：Substituting the values of $a$ , $b$ , and $c$ into the quadratic formula, we get two solutions for $t$ , $t 1 = 0.52$ and $t 2 = 13.48$ .

Step 5 ：Final Answer: The values of $t$ for which the rocket's height is 35 meters are $0.52$ seconds or $13.48$ seconds.

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