Please help me to to solve this quadratic equation word problem. Here is the question:
Studying Microgravity. NASA'S Glen Research Center in Cleveland, Ohio, has a 435-foot drop tower that begins on the surface and descends into Earth like a mineshaft. How long will it take a sealed container to fall 435 feet? Round to the nearest tenth of a second.
review your equation of motion. the distance is
s = 1/2 at^2
You know s=435 and a=-9.8
So, just find t.
To solve this quadratic equation word problem, we need to first determine the relevant equation that describes the situation. In this case, we can use the equation for the distance fallen by an object under the force of gravity:
d = 1/2 * g * t^2
where:
- d is the distance fallen (435 feet in this case),
- g is the acceleration due to gravity (32.2 feet/second^2), and
- t is the time for the fall.
We can rearrange the equation to solve for t:
t^2 = 2d / g
Now, let's substitute the given values into the equation:
t^2 = 2 * 435 / 32.2
t^2 ≈ 27
To find the value of t, we take the square root of both sides:
t ≈ √27
t ≈ 5.2 seconds (rounded to the nearest tenth)
Therefore, it will take the sealed container approximately 5.2 seconds to fall 435 feet in the NASA Glenn Research Center's drop tower.