Question

If a stone is thrown upward with a speed of 110 feet per second from a height of 500 feet above the surface of a planet, the equation h = 500 + 110t - 5.5t² approximates the height of the stone, in feet, at t seconds. When will the stone be 698 feet above the planet's surface?​

Answer 1

We can solve for the time when the stone will be 698 feet above the planet's surface by setting h = 698 and solving for t in the equation h = 500 + 110t - 5.5t²:

698 = 500 + 110t - 5.5t²

Rearranging, we get:

5.5t² - 110t + 198 = 0

Dividing both sides by 5.5, we get:

t² - 20t + 36 = 0

This is a quadratic equation that we can solve using the quadratic formula:

t = (-(-20) ± sqrt((-20)² - 4(1)(36))) / (2(1))

Simplifying, we get:

t = (20 ± sqrt(64)) / 2

t = 10 ± 4

So the possible values of t are t = 14 or t = 6. We can check which value is correct by plugging each value into the original equation and seeing if it gives a height of 698:

When t = 14:

h = 500 + 110(14) - 5.5(14)²

h = 500 + 1540 - 1078

h = 962

When t = 6:

h = 500 + 110(6) - 5.5(6)²

h = 500 + 660 - 198

h = 962

So both values of t give a height of 698. Therefore, the stone will be 698 feet above the planet's surface at t = 6 seconds or t = 14 seconds.