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
Potassium hydroxide (KOH) and
hydrochloric acid (HCl) react in a beaker. They form potassium chloride (KCl)
and water (H2O). This type of reaction is a double replacement reaction wherein
the two principal reactants exchange after the reaction. The Cl will combine to
the K forming KCl and the H will add to the OH forming H2O.
The solution for this problem is:torque1 = torque2 = FL / 2
Torque 3 = Torque 4 = FL / 2 * sin (theta)
Torque 5 = 2 FL
Torque 6 = 0
So the order of the torques from smallest to largest is torque 6, (torque 3 and 4), (torque 1 and 2), torque 5.
Remember or just take note that sin (theta) < 1 is why 3 and 4 are less than 1 and 2.
Answer:
4.78 × 10⁻³ T.m²
Explanation:
The expression for the magnetic flux is given by
∅ = BAcosФ
where B = magnetic field strength
A = Area of circular loop = πr²
r = radius of the wire loop
substitute πr² for A in the first equation
∅ = Bπr²cosФ
∅ = 2.55 × 3.14 × 0.025² × cos 17.3°
∅ = 4.78 × 10⁻³ T.m²
OR
0.00478 T.m²
1. the amount of electric charge that they carried
2. the distance between them
