Answer: a) 3.85 days
b) 10.54 days
Explanation:-
Expression for rate law for first order kinetics is given by:

where,
k = rate constant = ?
t = time taken for decomposition = 3 days
a = let initial amount of the reactant = 100 g
a - x = amount left after decay process = 
First we have to calculate the rate constant, we use the formula :
Now put all the given values in above equation, we get


a) Half-life of radon-222:


Thus half-life of radon-222 is 3.85 days.
b) Time taken for the sample to decay to 15% of its original amount:
where,
k = rate constant = 
t = time taken for decomposition = ?
a = let initial amount of the reactant = 100 g
a - x = amount left after decay process = 


Thus it will take 10.54 days for the sample to decay to 15% of its original amount.
Here we have perfectly inelastic collision. Perfectly inelastic collision is type of collision during which two objects collide, stay connected and momentum is conserved. Formula used for conservation of momentum is:

In case of perfectly inelastic collision v'1 and v'2 are same.
We are given information:
m₁=0.5kg
m₂=0.8kg
v₁=3m/s
v₂=2m/s
v'₁=v'₂=x
0.5*3 + 0.8*2 = 0.5*x + 0.8*x
1.5 + 1.6 = 1.3x
3.1 = 1.3x
x = 2.4 m/s
Answer:
Change/ Potential
Explanation:
Work is the amount of energy required to perform an action that is for a force to cause a displacement.
From work-energy theorem, work done by body is equal to change in its kinetic energy.
Work of gravity is basically the potential energy stored in the body due to gravity. From the law of conservation of mechanical energy, increased kinetic energy comes from the change of the potential energy of the stone.
It's a form of mechanical energy