Answer:
time taken is equal to 14,156 years
Explanation:
we know,

at t = 0
Y(0) = A
given that half life of plutonium 239 = 24,200



hence time taken is equal to 14,156 years
Answer:
The natural frequency = 50 rad/s = 7.96 Hz
Damping ratio = 0.5
Explanation:
The natural frequency is calculated in this manner
w = √(k/m)
k = spring constant = 5 N/m
m = mass = 2 g = 0.002 kg
w = √(5/0.002) = 50 rad/s
w = 2πf
50 = 2πf
f = 50/(2π) = 7.96 Hz
Damping ratio = c/[2√(mk)] = 0.1/(2 × √(5 × 0.002)) = 0.5
Answer:

Explanation:
Given that :
mass of the SUV is = 2140 kg
moment of inertia about G , i.e
= 875 kg.m²
We know from the conservation of angular momentum that:

![mv_1 *0.765 = [I+m(0.765^2+0.895^2)] \omega_2](https://tex.z-dn.net/?f=mv_1%20%2A0.765%20%3D%20%5BI%2Bm%280.765%5E2%2B0.895%5E2%29%5D%20%5Comega_2)
![2140v_1*0.765 = [875+2140(0.765^2+0.895^2)] \omega_2](https://tex.z-dn.net/?f=2140v_1%2A0.765%20%3D%20%5B875%2B2140%280.765%5E2%2B0.895%5E2%29%5D%20%5Comega_2)



From the conservation of energy as well;we have :

^2 -2140(9.81)[\sqrt{0.76^2+0.895^2} -0.765]] =0](https://tex.z-dn.net/?f=%5B%5Cfrac%7B1%7D%7B2%7D%20%5B875%2B2140%280.765%5E2%2B0.895%5E2%29%5D%280.4262%20%5C%20v_1%29%5E2%20-2140%289.81%29%5B%5Csqrt%7B0.76%5E2%2B0.895%5E2%7D%20-0.765%5D%5D%20%3D0)






the answer Is C. ,, thank you :)