An elevator moves downward in a tall building at a constantspeed of 5.00 m/s. Ex

Question

An elevator moves downward in a tall building at a constantspeed of 5.00 m/s. Exactly 5.00 s after the top of the elevator carpasses a bolt loosely attached to the wall of the elevator shaft,the bolt falls from rest. a) At what time does the bolt hit the top of thestill-descending elevator? c) Estimate the highest floor from which the bolt can fall ifthe elevator reaches the ground floor before the bolt hits the topof the elevator. An elevator moves downward in a tall building at a constantspeed of 5.00 m/s. Exactly 5.00 s after the top of the elevator carpasses a bolt loosely attached to the wall of the elevator shaft,the bolt falls from rest. a) At what time does the bolt hit the top of thestill-descending elevator? c) Estimate the highest floor from which the bolt can fall ifthe elevator reaches the ground floor before the bolt hits the topof the elevator.

Explanation / Answer

a)Let the time at which the bolt hit the top of the still-descending elevator be t The velocity of the bolt after 5.00 s is v = u + gt where u = 0,g = 9.8 m/s2 and t = 5.00 s or v = 0 + 9.8 * 5.00 = 49 m/s The distance travelled by the elevator after 5.00 s is S = ut + (1/2)gt2 ----------(1) where u = 5.00 m/s We know from the relation S = vt + (1/2)gt2 where S is obtained from equation (1)and v = 49 m/s. Solving the above equation for t we get the time. c)Let the highest floor from which the bolt can fall when the elevator comes to ground floor be S1 We know that v2 - u2 = 2gS1 or S1 = (u2/2g) or S1 = (u2/2g) where v = 0 and u = 49 m/s or S1 = 122.5 m

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