Derive the equation of motion fora particle falling vertically
Answers
Explanation:
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If the particle is thrown with initial velocity ‘u’ downward which is in negative y – axis, then velocity and position at of the particle any time t is given by v = u + gt v = ut + – gt2 The square of the speed of the particle when it is at a distance y from the hill – top is V2 = u2 + 2gy Suppose the particle starts from rest. Then u = 0 Then the velocity v2, the position of the particle and v at any time t are given by (for a point y from the hill – top) v = gt …………(i) y = 1 2 12 – gt2 …………(ii) v2 = 2gy …………(iii) The time (t = T) taken by the particle to reach the ground (for which y = h), is given by using equation (ii), h = 1 2 12– gT2 …………(iv) T = √ 2 h g 2hg …………(v) The equation (iv) implies that greater the height (h), particle takes more time (T) to reach the ground. For lesser height (h), it takes lesser time to reach the ground. The speed of the particle when it reaches the ground (y = h) can be found using equation (iii), we get, v g r o u n d vground = √ 2 g h 2gh …………(vi) The above equation implies that the body falling from greater height (h) will have higher velocity when it reaches the ground. The motion of a body falling towards the Earth from a small altitude (h<