A fossil mammoth bone was found to contain 6.25% carbon-14 percent isotope and 93.75% nitrogen-14 daughter isotope. If the half-life of carbon-14 is 5700 years old, how old is the mammoth bone?

The mammoth bone is 22726 years old.

Explanation:

We can find how hold is the mammoth bone using the decay equation:

  (1)

Where:

N(t): is the quantity at time t = 6.25%N₀

N₀: is the initial quantity

λ: is the decay constant

First, we need to find λ:

Now, by solving equation (1) for t we have:

Therefore, the mammoth bone is 22726 years old.

I hope it helps you!

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft