Motion In A Straight Line

Time taken by the bomb to reach the ground is given by

we have
Given,

Horizontal velocity of bomb
Horizontal distance covered by the bomb



Hence, the bomb-should be dropped before the target.

Given
Velocity (v) is defined as rate of change of displacement, also
using we have
hence
Initial velocity at t = 0, is

Also acceleration a =

Key Idea : The average velocity is defined as total displacement of the body in a particular time interval divided by the time interval.
Displacement from to
Displacement from to
Displacement from to
and displacement from to
Net displacement

Total time taken
Hence, average velocity

Key Idea : Applying conservation of energy. By law of conservation of energy


Since,

As v = 0 + na a =
and distance travelled in (n-2) second is

So distance travelled in the last 2 s is

From equation of motion, we have

where is displacement, is initial velocity, a is acceleration and is time.
When ,
we have


(i)
When body travels a total distance of min , we get


(ii)
Solving Eqs. (i) and (ii), we get

Given,
or
Integrating, we get

or
Again

Integrating again, we get


when,