Question

Gravity on the moon is about one- sixth of gravity on Earth. An astronaut standing on a tower 20 eet above the moon's surface throws a ball upward with a velocity of 30 feet per second. The height of the all at any time t (in seconds) is h(t) = -2.67t^2 + 30t + 20. To the nearest tenth of a second, how long will it take for the ball to hit the ground?

Answer 1

Answer on question 36946 – Math – Algebra

Gravity on the moon is about one-sixth of gravity on Earth. An astronaut standing on a tower 20 feet above the moon's surface throws a ball upward with a velocity of 30 feet per second. The height of the all at any time $t$ (in seconds) is $h(t) = -2.67t^2 + 30t + 20$. To the nearest tenth of a second, how long will it take for the ball to hit the ground?

Solution

In another word we should find the time when $h(t)$ equals 0. Therefore we get equation

$$-2.67t^2 + 30t + 20 = 0$$ $$D = 900 + 4 * 20 * 2.67 = 1113.6$$ $$t_1 = \frac{-30 - \sqrt{1113.6}}{-2 * 2.67} \approx 11.9 \text{ sec.}$$ $$t_2 = \frac{-30 + \sqrt{1113.6}}{-2 * 2.67} < 0.$$

Answer: 11.9 sec.