Question

A carpenter dropped a hammer from a rooftop 80 feet above the ground. How long did it take the hammer to pass by the 3rd floor window that is 32 feet off the ground? Round your answer to the nearest tenth.Recall the equation for falling objects: h(t)= h - 16t².where h(t) is the height of the object in feet, at any time t in seconds, and h₀ is the object's initial height in feet.

A. t = 16 seconds
B. t = 1.7 seconds
C. t = 3 seconds
D. t = 2.1 seconds

Answer 1

Using the equation for falling objects, we set h(t) to 32 feet for the 3rd floor window, and solve the equation 32 = 80 - 16t² to find that it takes approximately 1.7 seconds for the hammer to pass by the window.

Step-by-step explanation:

To find out how long it took the hammer to pass by the 3rd floor window, we can use the equation for falling objects: h(t) = h - 16t², where h(t) is the height of the object in feet at any time t in seconds, and h is the object's initial height in feet. To solve for t, we set h(t) equal to 32 feet, as this is the height of the 3rd floor window. The initial height, h, is 80 feet.

Now, we plug the values into the equation: 32 = 80 - 16t². Solving for t gives us 48 = 16t². Dividing both sides by 16, we get 3 = t². Taking the square root of both sides, we find that t is approximately 1.7 seconds. Therefore, the hammer took around 1.7 seconds to pass by the 3rd floor window. The correct option is B. t = 1.7 seconds.