During the construction of an office building, a hammer is accidentally dropped from a height of 784 ft. the distance (in feet)

Question

gregori

1 month ago

5

During the construction of an office building, a hammer is accidentally dropped from a height of 784 ft. the distance (in feet)

the hammer falls in t sec is s = 16t2. what is the hammer's velocity when it strikes the ground?

Physics

2 answers:

Softa [3K] · Answer 1 · 2026-04-05T18:03:48+03:00

Softa [3K]1 month ago

7 0

T= 24.5 feet per second. That’s the speed it attains just before hitting the ground.

Keith_Richards [3.2K] · Answer 2 · 2026-04-05T18:03:07+03:00

Response:

The speed at which the hammer strikes the ground is 128 ft/s.

Justification:

Given the following,

The distance (in feet) the hammer descends in t seconds is defined by the equation:

$s=16t^2$

Since the hammer was dropped from a height of 784 ft, we need to calculate the speed it reaches upon impact. We understand that the speed of an object is equal to:

$v=\dfrac{ds}{dt}\\\\v=\dfrac{d(16t^2)}{dt}\\\\v=32t$

When the hammer reaches the ground, s = 256 ft

Thus,

$16t^2=256\\\\t^2=16\\\\t=4\ s$

Therefore, the hammer's velocity while hitting the ground is calculated as:

$v=32t=32\times 4\\\\v=128\ ft/s$

Consequently, the hammer's speed upon striking the ground is 128 ft/s. This is the needed answer.