Answer:
Explanation:
The formula for this, the easy one, is
where No is the initial amount of the element, t is the time in years, and H is the half life. Filling in:
and simplifying a bit:
and
N = 48.0(.0625) so
N = 3 mg left after 12.3 years
Answer:
a) x(t) = 10t + (2/3)*t^3
b) x*(0.1875) = 10.18 m
Explanation:
Note: The position of the horse is x = 2m. There is a typing error in the question. Otherwise, The solution to cubic equation holds a negative value of time t.
Given:
- v(t) = 10 + 2*t^2 (radar gun)
- x*(t) = 10 + 5t^2 + 3t^3 (our coordinate)
Find:
-The position x of horse as a function of time t in radar system.
-The position of the horse at x = 2m in our coordinate system
Solution:
- The position of horse according to radar gun:
v(t) = dx / dt = 10 + 2*t^2
- Separate variables:
dx = (10 + 2*t^2).dt
- Integrate over interval x = 0 @ t= 0
x(t) = 10t + (2/3)*t^3
- time @ x = 2 :
2 = 10t + (2/3)*t^3
0 = 10t + (2/3)*t^3 + 2
- solve for t:
t = 0.1875 s
- Evaluate x* at t = 0.1875 s
x*(0.1875) = 10 + 5(0.1875)^2 + 3(0.1875)^3
x*(0.1875) = 10.18 m
Answer:
33.33j+6.67i km/hr
Explanation:
From the law of conservation of momentum,
Applying,
mu+m'u' = V(m+m')............... Equation 1
Where m = mass of the truck, m' = mass of the car, u = initial velocity of the truck, u' = initial velocity of the car, V = Final velocity.
Note: let j represent the north, and i represent the east
From the question,
Given: m = 1500 kg, u = 60j, m' = 1200 kg, u' = 15i
Substitute these values into equation 1
1500*60j+1200*15i = V(1500+1200)
90000j+18000i = 2700V
V = (90000j+18000i)/2700
V = 33.33j+6.67i km/hr
