Which scientist first proposed physical laws to mathematically describe the effect of forces on the motions of bodies?
2 answers:
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(a) The distance will be more than 2.0 meters.
In fact, you starts your fall after your friend has already fallen 2.0 meters. This means that your friend has already accelerated for a while, therefore his velocity will be greater than yours. But this statement will be actually true for the entire fall, since you has some delay, therefore when your friend will hit the water, the separation between you and him will be greater than the initial separation of 2.0 meters.
b) First of all we need to calculate the height of the bridge with respect to the water. We know that you take 1.6 s to fall down, therefore we can use the following equation:
We know that your friend will take 1.6 s to falls down. Instead, you start your jump after he has already fallen 2.0 m, therefore after a time given by the equation:
Using S=2.0 m,
So we know that you start your fall 0.64 s after your friend. Therefore, now we can find how much did you fall between the moment you started your fall (0.64 s) and the moment your friend hits the water (1.6 s). Using
we find
So, when your friend hits the water, you just covered 4.52 m, while he already covered 12.56 m. Therefore, the separation between you and your friend is more than 2 meters.
First, let's find the speed 
of the two blocks m1 and m2 sticked together after the collision.
We can use the conservation of momentum to solve this part. Initially, block 2 is stationary, so only block 1 has momentum different from zero, and it is:
After the collision, the two blocks stick together and so now they have mass
and they are moving with speed :
For conservation of momentum
So we can write
From which we find
The two blocks enter the rough path with this velocity, then they are decelerated because of the frictional force
. The work done by the frictional force to stop the two blocks is
where d is the distance covered by the two blocks before stopping.
The initial kinetic energy of the two blocks together, just before entering the rough path, is
When the two blocks stop, all this kinetic energy is lost, because their velocity becomes zero; for the work-energy theorem, the loss in kinetic energy must be equal to the work done by the frictional force:
From which we can find the value of the coefficient of kinetic friction:
We can use the conservation of momentum to solve this part. Initially, block 2 is stationary, so only block 1 has momentum different from zero, and it is:
After the collision, the two blocks stick together and so now they have mass
For conservation of momentum
So we can write
From which we find
The two blocks enter the rough path with this velocity, then they are decelerated because of the frictional force
where d is the distance covered by the two blocks before stopping.
The initial kinetic energy of the two blocks together, just before entering the rough path, is
When the two blocks stop, all this kinetic energy is lost, because their velocity becomes zero; for the work-energy theorem, the loss in kinetic energy must be equal to the work done by the frictional force:
From which we can find the value of the coefficient of kinetic friction: