With what initial speed should a body be thrown vertically downward from a height of h = 19.6 m so that it falls on a delta t = 1 s faster than a body that freely falls from the same height?
h = 19.6 meters – the height from which the body is thrown;
g = 9.8 Newton / kilogram – acceleration of gravity;
dt = 1 second – time span.
It is required to determine v0 (m / s) – with what initial speed the body must be thrown so that it falls dt seconds faster than the body, which freely falls from the same height.
Let us determine the time it takes for a freely falling body to fall:
t = (2 * h / g) ^ 0.5 = (2 * 19.6 / 9.8) ^ 0.5 = (39.2 / 9.8) ^ 0.5 = 4 ^ 0.5 = 2 seconds.
Then, the body must fall in a time equal to:
t1 = t – dt = 2 – 1 = 1 second.
The initial speed will be equal to:
h = v0 * t + g * t2 / 2;
v0 * t = h – g * t2 / 2;
v0 = h / t – g * t / 2 = 19.6 / 1 – 9.8 * 1/2 = 19.6 – 4.9 = 14.7 m / s.
Answer: the body must be thrown at a speed equal to 14.7 m / s.
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