How long will take the flower pot to hit the ground? algebra help needed

Question

A flower pot is tossed off a balcony it's height (in feet) is given by the formula h(t)=-16t^2+9.4t+90 where t is measured in seconds how long will it take the flower pot to hit the ground? round your answers to three decimal places. _____ seconds

Answer 1

To determine the time it takes for the flower pot to hit the ground, we need to find the moment when the height (h) of the pot is equal to zero. At this point (h = 0), the flower pot will have reached the ground.

Given that the formula for the height of the flower pot is:

h(t) = -16t²+ 9.4t + 90

We can set the height equation (h(t)) to 0:

0 = -16t² + 9.4t + 90

Now we have a quadratic equation in the form of at² + bt + c = 0, where a = -16, b = 9.4, and c = 90. In this case, we can use the quadratic formula to solve for t:

t = (-b ± √(b² - 4ac)) / (2a)

Substituting the values into the formula, we get:

t = (-9.4 ± √(9.4² - 4(-16)(90))) / (2(-16))

Simplify:

t = (-9.4 ± √(88.36 + 5760)) / (-32)

t = (-9.4 ± √(5848.36)) / (-32)

Now we calculate the square root:

t = (-9.4 ± 76.475) / (-32)

This gives us two possible solutions:

t₁ = (-9.4 + 76.475) / (-32) ≈ -2.096 seconds

t₂ = (-9.4 - 76.475) / (-32) ≈ 2.683 seconds

Notice the value of t₁. In the context of this problem, it would not make sense to have a negative value for time, so we classify -2.096 as an extraneous value. On the other hand, our value for t₂ seems to make perfect sense. Hence, it will take about 2.683 seconds for the flower pot the hit the ground.

Answer 2

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