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Two coconuts fall from rest at the same time, one from a treetwice as high as th

ID: 1734107 • Letter: T

Question

Two coconuts fall from rest at the same time, one from a treetwice as high as the other. If the coconut from the taller treereaches the ground with a speed of V, what will the speed of thecoconut from the other tree be when it reaches the ground? Second part is if the coconut from the shorter treetakes time T to reach the ground, how long (in terms of T) will ittake the other coconut to reach the ground? I am assuming there is a formula for this...anyideas? Two coconuts fall from rest at the same time, one from a treetwice as high as the other. If the coconut from the taller treereaches the ground with a speed of V, what will the speed of thecoconut from the other tree be when it reaches the ground? Second part is if the coconut from the shorter treetakes time T to reach the ground, how long (in terms of T) will ittake the other coconut to reach the ground? I am assuming there is a formula for this...anyideas?

Explanation / Answer

Speed of the coconut when it reach the ground v =[ 2gh ] Speed of the coconut from taller tree is   v i.e. v = [ 2gh ] Speed of the coconut from shorter tree v ' = [ 2g( h / 2 )]             Since the height of the smaller tree = ( 1/ 2) height of tallertree                                                                    = 0.707 [ 2gh ]                                                                    = 0.707 v (b). Time taken by the coconut to reach the ground fromheighest point t = [ 2 h / g ] Time taken for coconut from shorter tree  T =[ 2 ( h / 2 ) / g ]                                                                       = [ h / g ] So, time taken for the coconut from taller tree t ' = [ 2h / g ]                                                                               = 2 * T                                                                               = 1.414 T
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