Question

a lift is descending with uniform acceleration . To measure the acceleration ,a person in the lift drops a coin at the moment when lift was descending with speed
6ft/sec .The coin is 5 ft above the floor of the lift at the time it is dropped the person observes that the coin strikes the floor in 1 sec . Calculate the acceleration of the lift in ft/s^2

Answer 1

Person drops the coin at the moment when lift was descending with speed 6ft/s
so, initial velocity of coin with respect to lift = initial velocity of coin - initial velocity of lift = 0 - 6 = - 6ft/s .

Let acceleration of lift is n ft/s²
so, acceleration of coin with respect to lift = acceleration of coin - acceleration of lift
=( g - n) ft /s² [ here g is Acceleration due to gravity , g = 32ft/s²]
= (32 - n) ft/s²

Now, use formula,
S = ut + 1/2 at²
Here, S = 5ft , u = -6ft , a = (32 - n) , t = 1sec
∴ 5 = -6 × 1 + 1/2(32 - n) × 1²
⇒ 11 = 1/2(32 - n)
⇒22 = 32 - n
⇒ n = 10 ft/s²

Hence, acceleration of lift is 10 ft/s²

Answer 2

Hello Dear.


A lift is descending with a uniform acceleration let say it as a ft/s².

When the coin is dropped in the lift, if falls freely under gravity. Thus, its acceleration with Respect to the Ground is same as the acceleration due to gravity, g.
Acceleration due to gravity = 9.8 m/s²
 = 32 ft/s².

∵ Acceleration of the the Lift = Acceleration of the Coin with Respect to the Ground - Acceleration of the Coinwith Respect to the lift.

∴ Acceleration of the Coin with Respect to the lift = Acceleration of the Coin with Respect to the Ground - Acceleration of the Lift.

∴ Acceleration of the Coin with Respect to the lift = (g - a) ft/s².
    = (32 - a)ft/s²
   
Now, 
Time taken by the Coin to strikes the Ground (t) = 1 seconds.
Distance covered by the coin before striking the ground (h) = 5 ft.

 Initial Velocity(u) of the coin with respect to the lift = 0


Now,
Using the Second Equation of the Motion,

H = ut + (1/2)a₁t².
Where,
a₁ = acceleration of the Coin with respect to the lift.

5 = 0 + (1/2)a₁(1)²
⇒ 5 = 0 + a₁/2
⇒ a₁ =  10
⇒ a₁ = 10  ft/s².


Now, Acceleration of the Coin with respect to 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.


Have a Nice Day.