a body dropped from a height falls 16 feet during the first second, 48 feet the second second, 80 feet the third second, and so on. Find how far the body falls during the 7th second and how far it falls during the first 7 seconds
d = 16 t^2
at t = 6, d = 16*36 = 576
at t = 7, d = 16*49 = 784
784 - 576 = 208
ewjhfkshfksjhfkjshdfksjdhfkjshdfkjs
To find out how far the body falls during the 7th second, we can observe that the distance fallen during each second follows a pattern. In this case, the difference in distance fallen between successive seconds is increasing by 32 feet each time. So, during the 7th second, the body would have fallen an additional 32 feet compared to the 6th second.
To calculate the distance fallen during the 7th second, we add the additional 32 feet to the distance fallen during the 6th second, which is 80 feet.
Therefore, during the 7th second, the body falls a total of 80 + 32 = 112 feet.
To find out how far the body falls during the first 7 seconds, we need to sum up the distances fallen during each of the first 7 seconds.
The distance fallen during each second can be found using the formula for the distance traveled by a falling object:
d = (1/2) * g * t^2
where d is the distance fallen, g is the acceleration due to gravity (32 ft/s^2 on Earth), and t is the time in seconds.
For the first second, the distance fallen is given as 16 feet.
d1 = (1/2) * 32 * 1^2 = 16 feet
For the second second, the distance fallen is given as 48 feet.
d2 = (1/2) * 32 * 2^2 = 48 feet
For the third second, the distance fallen is given as 80 feet.
d3 = (1/2) * 32 * 3^2 = 80 feet
Following this pattern, we can calculate the distances fallen during the next seconds:
d4 = (1/2) * 32 * 4^2 = 128 feet
d5 = (1/2) * 32 * 5^2 = 200 feet
d6 = (1/2) * 32 * 6^2 = 288 feet
d7 = (1/2) * 32 * 7^2 = 392 feet
Finally, to find the total distance fallen during the first 7 seconds, we add up all these distances:
Total distance fallen = d1 + d2 + d3 + d4 + d5 + d6 + d7
= 16 + 48 + 80 + 128 + 200 + 288 + 392
= 1152 feet
Therefore, the body falls a total of 1152 feet during the first 7 seconds.