Via the half-life equation:

Where the time elapse is 11,460 year and the half-life is 5,730 years.

Therefore after 11,460 years the amount of carbon-14 is one fourth (1/4) of the original amount.
Explanation:
Given Data
Total mass=93.5 kg
Rock mass=0.310 kg
Initially wagon speed=0.540 m/s
rock speed=16.5 m/s
To Find
The speed of the wagon
Solution
As the wagon rolls, momentum is given as
P=mv
where
m is mass
v is speed
put the values
P=93.5kg × 0.540 m/s
P =50.49 kg×m/s
Now we have to find the momentum of rock
momentum of rock = mv
momentum of rock = (0.310kg)×(16.5 m/s)
momentum of rock =5.115 kg×m/s
From the conservation of momentum we can find the wagons momentum So
wagon momentum=50.49 -5.115 = 45.375 kg×m/s
Speed of wagon = wagon momentum/(total mass-rock mass)
Speed of wagon=45.375/(93.5-0.310)
Speed of wagon= 0.487 m/s
Throwing rock backward,
momentum of wagon = 50.49+5.115 = 55.605 kg×m/s
Speed of wagon = wagon momentum/(total mass-rock mass)
speed of wagon = 55.605 kg×m/s/(93.5kg-0.310kg)
speed of wagon= 0.5967 m/s
Answer:
246.28 K
Explanation:
The total energy of one mole of gas molecules can be calculated by the formula given below
E = 
Where R is gas constant and T is absolute temperature.
Put the value of R as 8.314 and temperature as 245 , we get
E = 
= 3055.4 J
Add 16 j to it
Total energy of gas molecules = 3055.4 + 16 = 3071.4 J.
If T be the temperature after addition of energy then
= 3071.4
T =
T = 246.28 K
Theoretically, if the objects have the same mass and are moving towards each other at a speed of

, after a perfectly elastic collision, the object A is supposed to move with the same velocity in the opposite direction.