Question

Mr. B revealed during our advisory meeting that he once fell through a plate glass window from the fourth story of the factory building. That is about 40 feet in the air. How long did it take for him to hit the ground? (Recall: Position formula ➔ X(t) = -16t2 + V0t + h0 ➔ Assume V0 = 0)

Answer 1

To determine the time it took for Mr. B to hit the ground from a height of 40 feet, the free fall position formula is used. By setting the equation -16t^2 + 40 = 0 and solving for t, we find that it took approximately 1.58 seconds to reach the ground.

Step-by-step explanation:

The question pertains to the free fall of an object in physics. Given the initial velocity (V0) is 0 and the starting height (h0) is 40 feet, we can apply the position formula for free fall, which is X(t) = -16t2 + V0t + h0. To find the time taken for Mr. B to hit the ground, we need to solve for t when X(t) equals zero (at ground level).

Setting up the equation 0 = -16t2 + 0t + 40 simplifies to 0 = -16t2 + 40, which can further be simplified to 16t2 = 40 by bringing the terms to one side. Dividing both sides by 16 gives t2 = 40/16, or t2 = 2.5. Taking the square root of both sides gives us t ≈ 1.58 seconds. Therefore, it took approximately 1.58 seconds for Mr. B to hit the ground after falling from a fourth-story window.

Answer 2

It took approximately 1.1 seconds for Mr. B to hit the ground after falling through the plate glass window from the fourth story of the factory building.

Step-by-step explanation:

To determine how long it took for Mr. B to hit the ground after falling through the plate glass window, we can use the equation of motion for free fall: X(t) = -16t^2 + V0t + h0. In this equation, V0 represents the initial velocity, which is 0 in this case because Mr. B fell without any initial upward or downward velocity. h0 represents the initial height, which is 40 feet or 12.19 meters. Setting X(t) = 0, we can solve for t:

0 = -16t^2 + 0t + 12.19

16t^2 = 12.19

t^2 = 12.19/16

t = sqrt(12.19/16) ≈ 1.1 seconds

Therefore, it took approximately 1.1 seconds for Mr. B to hit the ground.