The distance s in feet that a body falls in t seconds is given by the formula s=16t^2. If a body has been falling for 5 seconds, how far will it fall during the 6th second
at 5 seconds it has fallen 16 * 25
at 6 seconds it has fallen 16 * 36
so
between 5 and 6 it falls
16(36-25)
To find out how far a body will fall during the 6th second, we can start by calculating the distance it has already fallen in the first 5 seconds.
Using the formula s = 16t^2, we can calculate the distance fallen in each second:
- For t = 1: s = 16(1^2) = 16 feet
- For t = 2: s = 16(2^2) = 64 feet
- For t = 3: s = 16(3^2) = 144 feet
- For t = 4: s = 16(4^2) = 256 feet
- For t = 5: s = 16(5^2) = 400 feet
Since the body has been falling for 5 seconds, it has already fallen a distance of 400 feet.
To find how far it will fall during the 6th second, we need to subtract the distance fallen in 5 seconds from the distance fallen in 6 seconds.
For t = 6: s = 16(6^2) = 576 feet
Therefore, during the 6th second, the body will fall an additional distance of 576 - 400 = 176 feet.
To find out how far the body will fall during the 6th second, we need to determine the distance it has already fallen after 5 seconds.
Given that the formula for distance is s = 16t^2, we can substitute t = 5 into the formula:
s = 16 * (5)^2
s = 16 * 25
s = 400 feet
So after 5 seconds, the body has fallen 400 feet.
Now, to calculate the distance the body will fall during the 6th second, we need to find the difference between the distance after 6 seconds and the distance after 5 seconds.
Using the formula again, we can substitute t = 6 and t = 5 into the formula separately:
s_6 = 16 * (6)^2
s_5 = 16 * (5)^2
Now we subtract the distance after 5 seconds from the distance after 6 seconds:
s_6 - s_5 = (16 * (6)^2) - (16 * (5)^2)
= 16 * (36 - 25)
= 16 * 11
= 176 feet
Therefore, the body will fall 176 feet during the 6th second.