Motion In A Plane

From equation of motion

where is initial velocity and is time.
Since,

The horizontal range of the drop ,
then
Also,
Tangential speed


Locus of drop

Total distance covered by train is sum of train's length plus length of bridge.
Total time taken by train to cross the bridge

Total distance Length of train Length of bridge

Velocity of train

The necessary centripetal force to the coin is provided by the frictional force.
For moving on circular path without slipping, centripetal force must equal frictional force. That is,

Or

Or
Given,

or

At maximum height vertical component of final velocity is zero.
It is given velocity at half the height is .
From equation of motion, we have

where is final velocity,
is acceleration due to gravity and is displacement.
At maximum height


At half the height,

Now

Maximum height attained is

When the particle completes half revolution, change in velocity

Time taken to complete the half revolution is
second
Thus, average acceleration

As so these forces will be acting along the sides of a right angled triangle. Angle between 5 N and 13 N