If a stone is tossed from the top of a 250 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 250, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer

Dade County is not the subject.

Please show your own work if you need assistance.

All you have to do is solve

-9.8t^2 – 10t + 250 = 0

Use the quadratic formula

Actually the formula they gave you is wrong. The first term should be -4.9 t^2, not -9.8 t^2. The acceleration of gravity (g) must be divided by two in the coefficient of t^2.

The stone is evidently thrown with an initial downward velocity of 10 m/s

To find out how many seconds it will take for the stone to hit the ground, we need to determine when the height of the stone is zero. In the given equation, the height of the stone is represented by h(t).

Therefore, we can set h(t) = 0 and solve for t.

0 = -9.8t^2 - 10t + 250

To solve this quadratic equation, we can apply the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / 2a

Comparing the equation 0 = -9.8t^2 - 10t + 250 with ax^2 + bx + c = 0, we have:
a = -9.8, b = -10, c = 250

Substituting these values into the quadratic formula:

t = (-(-10) ± √((-10)^2 - 4*(-9.8)*250)) / (2*(-9.8))

Simplifying further:

t = (10 ± √(100 + 9800))/(-19.6)

Calculating inside the square root:

t = (10 ± √9900)/(-19.6)

Now, let's simplify the equation using a calculator:

t = (10 ± 99.5)/(-19.6)

For the positive solution:
t = (10 + 99.5)/(-19.6) ≈ -5.12 seconds

For the negative solution:
t = (10 - 99.5)/(-19.6) ≈ 5.07 seconds

Since we are only considering positive time, the stone will hit the ground after approximately 5.07 seconds.

Rounding to the nearest hundredth's place, the stone will hit the ground in about 5.07 seconds.