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A lift is descending with uniform acc. To measure the acc a person in the lift drops a coin at the moment at the moment when lift was descending with speed 6 ft / s. The coin is 5ft above the floor of the lift when it was dropped. The person observes that the coin strikes the floor in 1 sec. calculate the acc of the lift.

A lift is descending  with uniform acc. To measure the acc a person in the lift drops a coin at the moment  at the moment when lift was descending with speed 6 ft / s. The coin is 5ft above the floor of the lift when it was dropped. The person observes that the coin strikes the floor in 1 sec. calculate the acc of the lift.

Grade:11

1 Answers

Khimraj
3007 Points
5 years ago
cceleration due to gravity = 9.8 m/s² = 32 ft/s².
∵ Acceleration of the the Lift is equals to the 
= Acceleration of Coin w.r.t the Ground - Acceleration of the Coin w.r.t. the lift.
∴ Acceleration of the Coin w.r.t. the lift = Acceleration of the Coin w.r.t. the Ground - Acceleration of the Lift.
∴ Acceleration of the Coin w.r.t. the lift = (g - a) ft/s².    
   = (32 - a)ft/s²   
From the Question, 
Time taken by the Coin to strikes the Ground (t) = 1 seconds.
Distance covered through the coin before striking the ground (S) = 5 ft.
 Initial Velocity(u) of the coin w.r.t. the lift = 0
[Since, the coin starts from the rest.]

From the Second Equation of the Motion,
S = ut + (1/2)a₁t².
Where,
a₁ = acceleration of the Coin w.r.t. the lift.
5 = 0 + (1/2)a₁(1)² 
5 = 0 + a₁/2 
a₁ =  10 
a₁ = 10  ft/s².
Now, Acceleration of the Coin w.r.t. the lift = 10 ft/s².
∴  10 = 32 - a 
  a = 32 - 10 
  a =  22 ft/s².
∴ Acceleration of the lift is 22 ft/s².

Hope it helps.

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