A body falling from rest was observed to fall through 78.4 m in 2 seconds. Find how long had it been falling before it was observed? (g = 9.8 m/s2)A 5 seconds B 1 second C 3 seconds D 10 seconds
Question
A body falling from rest was observed to fall through 78.4 m in 2 seconds. Find how long had it been falling before it was observed? (g = 9.8 m/s2)A 5 seconds B 1 second C 3 seconds D 10 seconds
Solution
The problem involves the physics concept of free fall. The formula for the distance covered in free fall is given by:
d = 0.5 * g * t^2
where: d = distance (in meters) g = acceleration due to gravity (in m/s^2) t = time (in seconds)
We know that the body fell 78.4 m in 2 seconds. So, we can substitute these values into the formula to find the total time the body had been falling:
78.4 = 0.5 * 9.8 * t^2
Solving for t gives:
t^2 = 78.4 / (0.5 * 9.8) t^2 = 16 t = sqrt(16) t = 4 seconds
This means the body had been falling for 4 seconds in total. However, we know that the body was observed to fall for 2 seconds. Therefore, the body had been falling for 4 - 2 = 2 seconds before it was observed.
So, none of the options A, B, C, D are correct. The correct answer should be 2 seconds.
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