Question

A lift starts from rest at t = 0 and moves upwards with constant acceleration of 5 m/s2. At t = 2 s, a bolt
from the ceiling of lift detaches and falls freely. If height of lift is 7.5 m, then the bolt hits the floor of lift at
1= ns. Find the value of n. (g = 10 m/s2)​

Answer 1

Answer:

Explanation:

A lift starts from rest at t = 0 and moves upwards with constant acceleration of 5 m/s2. At t = 2 s, a bolt  from the ceiling of lift detaches and falls freely. If height of lift is 7.5 m, then the bolt hits the floor of lift at  1= ns. Find the value of n. (g = 10 m/s2)​

Lift starts from rest

u = 0 m/s

after t = 2sec

a = 5 m/s²

v = u + at = 0 + 5*2 = 10 m/s

Bolt hits the floor in n sec

Bolt initial speed = 0 m/s

a = 10 m/s²

S = ut + (1/2)at²

=> S bolt = 0 + (1/2)(10)n²

=> S bolt = 5n²

SLift = 10n + (1/2)5n²

=> SLift = 10n + 2.5n²

S bolt + Slift = 7.5

=> 5n² + 10n + 2.5n² = 7.5

=> 7.5n² + 10n  - 7.5 = 0

=>  3n² + 4n - 3 = 0

=> n = 0.535 sec