The total distance traveled by the object is 3h.
The total distance traveled by the object can be determined by applying the principle of conservation of energy as follows;
Since the object loses half its energy each time it hits the ground.
Hence it will rise half of the previous height each time, as potential energy at height h is given by;
P.E = mgh
Thus, the object will rise h/2 after the first hit, then h/4 and so on.
Hence the total distance traveled by the object is calculated as follows;
s = h + (h/2 + h/2 + h/4 + h/4 + ---)
s = h + (h + h/2 + ---)
s = h + h(1 + 1/2 + 1/4 + ---)
s = h + h(1 + (1/1 - 1/2) )
s = 3h
Thus, the total distance traveled by the object is 3h.
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The complete question is below:
An object is dropped from h height. graph v vs h? Every time it hits the ground it looses 50% of its kinetic energy. The total distance covered as t→∞ is :
