Two bodies begin to fall freely from the same height but 2nd one falls T seconds ater 1st.The time(after which the 1st body begin to fall) when the diatance between them is L is:
Options
1.T/2 2.T/2+L/gT 3.L/gT 4.T+2L/gT
I am not understanding how to find the time and what is the significance of L how to use ut!??
The problem is really worded poorly. It is asking if two objects are dropped at slightly different times, how does the length between them vary with time.
distancefirst=1/2 g t^2
distancesecond=1/2 g(t-T)^2
distance L= distancefirst-distancesecond
= 1/2 g (t^2-(t-T)^2)=L
so solve for t.
1/2 g (t^2-t^2+2tT-T^2)=L
1/2 g T(2t-T)=L
well, you can solve for time t.
To understand how to find the time and the significance of L in this scenario, let's break down the problem step by step.
First, let's define the variables used in the problem:
- T: The time delay between the two bodies, meaning the second body starts to fall T seconds after the first body.
- L: The distance between the two bodies at a given time.
- g: The acceleration due to gravity.
Now, let's consider the motion of the two bodies. Since both bodies are falling freely, they will be subject to the same acceleration due to gravity (represented by g). The distance traveled by a falling object is given by the formula:
d = (1/2)gt^2
Where d is the distance traveled, g is the acceleration due to gravity, and t is the time elapsed.
So, let's assume the first body starts falling at time t = 0. After T seconds, the second body starts falling. At this point, the first body will have traveled a distance of:
d1 = (1/2)g(0 + T)^2 = (1/2)gT^2
Now, let's find the time t when the distance between the two bodies is L. At time t, the first body will have traveled a distance of:
d1 = (1/2)gt^2
Similarly, at time t, the second body will have traveled a distance of:
d2 = (1/2)g(t - T)^2
The distance between the two bodies is L, so we have:
L = d1 - d2
= (1/2)gt^2 - (1/2)g(t - T)^2
Next, let's simplify the equation:
L = (1/2)gt^2 - (1/2)g(t^2 - 2tT + T^2)
= (1/2)g(2tT - T^2)
= g(tT - (1/2)T^2)
Now, let's solve for t:
L = g(tT - (1/2)T^2)
L/g = tT - (1/2)T^2
tT = L/g + (1/2)T^2
t = (L/gT) + (1/2)T
Therefore, the answer is option 2.T/2+L/gT.