A building is 862 feet tall. Use the function h(t) = 16t2 to approximate how long it would take an object to fall from the top.

Round to the nearest tenth.

Hint: h is your height.

So you are solving

16t^2 = 862
t^2 = 53.875
t = √53.875 = appr. 7.3 seconds

t =~ 7.3 seconds. Thank you that the same answer that I got.

To determine how long it would take an object to fall from the top of a building, we can set up the equation h(t) = 16t^2, where h(t) represents the height at time t and t represents the time in seconds.

In this case, the height of the building is given as 862 feet. We need to find the time it takes for an object to fall from the top to the ground, so we set h(t) = 0.

0 = 16t^2

Now we can solve for t.

Divide both sides of the equation by 16:
0 = t^2

Take the square root of both sides to isolate t:
0 = t

Since there are no real solutions for t in this equation, it suggests that the object would never hit the ground. However, this is not physically accurate, as we know that objects fall to the ground.

So it seems there is a mistake in the given function h(t) = 16t^2. The correct function to use for this problem would be h(t) = -16t^2, where the negative sign indicates downward motion.

Let's redo the calculations using the correct function:

0 = -16t^2

Divide both sides of the equation by -16:
0 = t^2

Take the square root of both sides to isolate t:
0 = t

Similar to the previous result, we get t = 0. This would imply that the object falls instantaneously, which is also inaccurate.

To provide a more realistic answer, we can consider the average speed of falling objects. On Earth, objects generally fall with an acceleration due to gravity of approximately 32 feet per second squared (32 ft/s^2). Taking this into account, we can modify the equation to:

h(t) = -16t^2

Setting h(t) = 862, we can solve for t:

862 = -16t^2

Divide both sides of the equation by -16:
-53.875 = t^2

Take the square root of both sides to isolate t:
t = √(-53.875)

Since the square root of a negative value is not a real number, it suggests that the object would never hit the ground.

However, with the assumption of a constant acceleration due to gravity, we can approximate the time it would take for the object to fall using this modified formula. However, this approximation is not entirely accurate.

If you have additional information or another function, please provide it so we can help you further.