An elevator is moving upward at a constant speed of 2.50 m/s. A bolt in the elev

ID: 582060 • Letter: A

Question

An elevator is moving upward at a constant speed of 2.50 m/s. A bolt in the elevator ceiling 3.00 m above the elevator floor works loose and falls.

A- How long does it take for the bolt to fall to the elevator floor?

B- What is the speed of the bolt just as it hits the elevator floor according to an observer in the elevator?

C- What is the speed of the bolt according to an observer standing on one of the floor landings of the building?

D- According to the observer in part C, what distance did the bolt travel between the ceiling and the floor of the elevator?

a) height = 3.00 m

h = ut + 1/2 *g*t^2

let's watch in elevator frame

u = 0 with respect to elevator

h = 1/2 *g*t^2

t = sqrt(2*h/g)

t = 0.775 second

b) Velociy v of bolt before hitting floor with respect to elevator frame

v = u + gt and u = 0

=> v1 = g*t = 10*0.775 = 7.75 m/s

accleration of bolt is same in both frames i.e. wrt ground or wrt elevator

so velocity before hitting floor wrt. observer on the ground = v1 - 2.5 = 5.25 m/s

d) distance travelled by bolt with respect to observer in part c

= 3 + 0.775*2.5 = 4.94 m

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