Answer:
The hammer's velocity when it strikes the ground is 128 ft/s.
Explanation:
Given that,
The distance (in feet) the hammer falls in t sec is given by the relation as :
[tex]s=16t^2[/tex]
The hammer is accidentally dropped from a height of 784 ft. We need to find the hammer's velocity when it strikes the ground. We know that the velocity of an object is equal to :
[tex]v=\dfrac{ds}{dt}\\\\v=\dfrac{d(16t^2)}{dt}\\\\v=32t[/tex]
When the hammer strikes ground, s = 256 ft
So,
[tex]16t^2=256\\\\t^2=16\\\\t=4\ s[/tex]
So, the velocity of the hammer when it strikes the ground is given by :
[tex]v=32t=32\times 4\\\\v=128\ ft/s[/tex]
So, the hammer's velocity when it strikes the ground is 128 ft/s. Hence, this is the required solution.
