Answer:
See explanation below.
Explanation:
For this case we atart fom the proportional model given by the following differential equation:
And if we rewrite this expression we got:
If we integrate both sides we got:
And using exponential on both sides we got:
Where represent the initial amount for the isotope and t the time in years and A the amount remaining.
If we want to apply a model for the half life we know that after some time definfd the amount remaining is the hal, so if we apply this we got:
We can cancel and we got:
If we solve for k we can apply natural log on both sides and we got:
And that would be our proportional constant on this case.
If we replace this value for k int our model we will see that:
And using properties of logs we can rewrite this like that:
And thats the common formula used for the helf life time.
Answer:
Explanation:
In projectile motion , formula for range is as follows
R = u² sin 2 α / g , where u is initial velocity of throw , α is angle of throw
Given R , range = 30 yards , α = 10°
30 = u² sin 20 / 9.8
u² x .342 = 294
u² = 859.65
u = 29.32 m / s
Answer:
Explanation:
We know that the gravity on the surface of the moon is,
<u>Gravity at a height h above the surface of the moon will be given as:</u>
..........................(1)
where:
G = universal gravitational constant
m = mass of the moon
r = radius of moon
We have:
- is the distance between the surface of the earth and the moon.
Now put the respective values in eq. (1)
is the gravity on the moon the earth-surface.