The time (t, in seconds) for a free-falling object to fall d feet is described by the mathematical formula:
t=d over the square root of 16
If a worker accidentally drops a hammer from a building and it hit the ground 4 seconds later, from what height was the hammer dropped
sqrt(16)=4
t=d/4
t=4
4=d/4
d=16
the hammar was dropped from 16 feet
your formula for time should have been:
t = √(d/16) or d = 16t^2
when t=4, then
d = 16(4^2) = 64 feet
To find the height from which the hammer was dropped, we can rearrange the formula and solve for d.
The formula for the time it takes for a free-falling object to fall is:
t = d / √16
Given that the hammer hits the ground in 4 seconds, we have:
4 = d / √16
To solve for d, we can isolate it by multiplying both sides of the equation by √16:
4 * √16 = d
Simplifying this expression:
4 * 4 = d
16 = d
Therefore, the hammer was dropped from a height of 16 feet.
To find the height from which the hammer was dropped, we need to rearrange the formula:
t = d / sqrt(16)
We can rewrite the formula as:
d = t * sqrt(16)
Substituting the given time (t = 4 seconds) into the formula:
d = 4 * sqrt(16)
Now, let's solve the equation step by step:
1. Calculate the square root of 16: sqrt(16) = 4
2. Multiply 4 by 4: 4 * 4 = 16
So, the height from which the hammer was dropped is 16 feet.