Answer:
the third piece landed
meters in a direction 45 degrees from the observer's right towards the front
Explanation:
Due to conservation of momentum, the momentum of the third piece must add to the other two momenta in vector from to render zero (initial momentum of the firework on a plane parallel to ground. Therefore the momentum components of the third piece must have a component to the right equal in magnitude to the momentum of the piece that traveled to the left, and a momentum component pointing to the front of the observer of equal magnitude to that of the piece that traveled behind the observer. Then the direction of the third momentum must be at 45 degrees from the observer's right towards the observer's front.
Also, the magnitude of a momentum vector of such components, is given by the Pythagorean theorem. Recall also that the magnitudes of the momentum vectors of the first two pieces must be equal since they traveled equal distances.

Then the distance traveled by the third piece must also keep this proportionality:

Answer:
I = 0.002593 A = 2.593 mA
Explanation:
Current density = J = (3.00 × 10⁸)r² = Br²
B = (3.00 × 10⁸) (for ease of calculations)
The current through outer section is given by
I = ∫ J dA
The elemental Area for the wire,
dA = 2πr dr
I = ∫ Br² (2πr dr)
I = ∫ 2Bπ r³ dr
I = 2Bπ ∫ r³ dr
I = 2Bπ [r⁴/4] (evaluating this integral from r = 0.900R to r = R]
I = (Bπ/2) [R⁴ - (0.9R)⁴]
I = (Bπ/2) [R⁴ - 0.6561R⁴]
I = (Bπ/2) (0.3439R⁴)
I = (Bπ) (0.17195R⁴)
Recall B = (3.00 × 10⁸)
R = 2.00 mm = 0.002 m
I = (3.00 × 10⁸ × π) [0.17195 × (0.002⁴)]
I = 0.0025929449 A = 0.002593 A = 2.593 mA
Hope this Helps!!!
East component: 3.9 m/s
South component: 1.8 m/s
Explanation:
We have to resolve the velocity vector along the east and south axis.
Taking east as positive x-direction and south as positive y-direction, the components of the velocity are given by:

where
v = 4.3 m/s is the magnitude of the velocity
is the angle between the direction of the velocity and of the x-axis
Substituting into the equations, we find:
East component:

South component:

Learn more about vector components:
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Answer:
The dominant feature in an open pit or quarry operation is the pit, a broad, deepened, often funnel-shaped area where overburden has been removed to access the material to be mined. This is where material extraction takes place.
Explanation:
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