Answer:
200 million years
Explanation:
The equation that describes the decay of a radioactive isotope is
where
is the amount of radioactive isotope left at time t
is the initial amount of isotope
is the half-life of the sample
In this problem, the ratio between unstable isotope and daughter isotope is 1:15; this means that
Because the "total proportion" of original sample was 1+15=16.
Also we know that the half-life is
So we can re-arrange the equation to find t, the age of the rock:
So, 200 million years.
<span>3598 seconds
The orbital period of a satellite is
u=GM
p = sqrt((4*pi/u)*a^3)
Where
p = period
u = standard gravitational parameter which is GM (gravitational constant multiplied by planet mass). This is a much better figure to use than GM because we know u to a higher level of precision than we know either G or M. After all, we can calculate it from observations of satellites. To illustrate the difference, we know GM for Mars to within 7 significant figures. However, we only know G to within 4 digits.
a = semi-major axis of orbit.
Since we haven't been given u, but instead have been given the much more inferior value of M, let's calculate u from the gravitational constant and M. So
u = 6.674x10^-11 m^3/(kg s^2) * 6.485x10^23 kg = 4.3281x10^13 m^3/s^2
The semi-major axis of the orbit is the altitude of the satellite plus the radius of the planet. So
150000 m + 3.396x10^6 m = 3.546x10^6 m
Substitute the known values into the equation for the period. So
p = sqrt((4 * pi / u) * a^3)
p = sqrt((4 * 3.14159 / 4.3281x10^13 m^3/s^2) * (3.546x10^6 m)^3)
p = sqrt((12.56636 / 4.3281x10^13 m^3/s^2) * 4.458782x10^19 m^3)
p = sqrt(2.9034357x10^-13 s^2/m^3 * 4.458782x10^19 m^3)
p = sqrt(1.2945785x10^7 s^2)
p = 3598.025212 s
Rounding to 4 significant figures, gives us 3598 seconds.</span>
Well, the spring constant is measured using the F=k∆x, where F is the force, k is the constant, and ∆x is the change in position. So if the mass is 1.98, the force (mxg) is 19.4. Thus the spring constant is 19.4/.0478(change in position). This equals 405.86.
Ke=34J. The canoe's kinetic energy floating downriver at a speed of 2m/s and 17kg mass is 34J.
This is a problem of kinetic energy, which is a form of energy, known as motion energy. The kinetic energy of an object is that which is produced because of its movements that depends on its mass and velocity.
The kinetic energy is represented by the following formula: Ke = ½ mv². The kinetic energy is measured in Joules (J), the mass in kilograms (kg) and the speed in meters over seconds (m/s).
A small 17kg canoe is floating downriver at a speed of 2m/s. Let's calculate canoe's kinetic energy.
Ke= (17kg)[(2m/s)²]/2= 68/2 kg m²/s²=34J
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