An elevator, in which a man is standing moving upward with a constant
speed of 10m/sec2. If a man drops a coin from a height of 2.5m. Find the time
taken by it to reach the oor of the elevation? g=9.8m/sec2
velocity of the lift (u₁) = 10 m/s
initial velocity of the coin (u₂) = 10 m/s
(the coin is also moving with the Elevator)
acceleration of the coin (a₂) = -9.8 m/s²
acceleration of the Elevator (a₁) = 0 m/s
Distance covered by the coin (s) = -2.5 m
Relative Velocity and Acceleration:Relative velocity:
We will find the velocity and acceleration of the coin with respect to the lift since we are monitoring the motion of the coin
velocity of the coin with respect to the elevator (u₂₁) = u₂ - u₁
u₂₁ = 10 - 10
u₂₁ = 0m/s
Relative Acceleration:
acceleration of the coin with respect to the elevator (a₂₁) = a₂ - a₁
a₂₁ = -9.8 - 0
a₂₁ = -9.8
Solving for the Time taken:From the second equation of motion, we know that:
s= ut + 1/2at₂
we can rewrite this equation in terms of relative motion:
s = u₂₁(t) + 1/2(a₁₂)t²
Notice that the time and the displacement are not relative, that's because displacement and time will remain the same no matter the frame of reference
replacing the known values in the equation:
-2.5 = (0)(t) + 1/2 (-9.8)(t²)
-2.5 = -4.9(t²)
dividing both sides by -4.9
t² = -2.5 / -4.9
t² = 25/49
t² = (5)² / (7)²
taking the square root of both the sides
t = 5/7 OR 0.71 seconds (approx)
Therefore, the coin will reach the floor of the Elevator in 0.71 seconds
when jerome paddle in flowing river towards east the net speed of jerome will increase
so the net speed of jerome will be given as
now the speed of paul will be same as it is given as he is running on the ground
so
so here we can say since the speed of jerome is more so he will win the race
now as we know the distance so the time difference is given as
so jerome will reach first and the time difference will be 203.55 s or 3.4 min