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Luden [163]
3 years ago
8

A lawyer drives from her​ home, located 1 mile east and 8 miles north of the town​ courthouse, to her​ office, located 4 miles w

est and 4 miles south of the courthouse. Find the distance between the​ lawyer's home and her office.
Physics
1 answer:
givi [52]3 years ago
4 0

Answer:

d = 13 miles

Explanation:

Lets say the position of court house is origin in this case

her office is located at 4 miles west and 4 miles south of court house

so here we have coordinate of the office with respect to court house is given as

r_1 = (-4\hat i - 4\hat j)

now the position of her home is located at 1 miles east and 8 miles north of the court house

so the coordinates of her home is given as

r_2 = (1\hat i + 8 \hat j)

now the change in the position is given as the distance between office and home

d = r_2 - r_1

d = 5 \hat i + 12 \hat j

d = \sqrt{5^2 + 12^2} = 13 miles

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A small fish is dropped by a pelican that is rising steadily at 0.50 m/s.
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Answer:

(a)  24.025 m/s. downward.

(b)  31 m

Explanation:

From Newton's equation of motion,

(a)

v = u + gt ................... Equation 1

Where v = final velocity, u = initial velocity, g = acceleration due to gravity, t = time.

Note: Let upward velocity be negative and downward be positive

Given: u = -0.5 m/s (upward), t = 2.5 s

Constant : g = 9.81 m/s²

Substitute into equation 1

v = 0.5+9.81(2.5)

v = -0.5+24.525

v = 24.025 m/s. downward.

(b) using

s₁ = ut + 1/2gt²......................... Equation 2

Where s₁ = distance at which the fish fall after being dropped by the pelican

Given: u = - 0.5 m/s, t = 2.5 s, g = 9.81 m/s²

Substitute into equation 2

s₁ = -0.5(2.5) + 1/2(9.81)(2.5)²

s₁ = -1.25+30.656

s₁ = 29.41 m

also,

s₂ = vt ................ Equation 3

Where s₂ = the distance by which the pelican rise during this time.

Given: v = 0.5 m/s, t= 2.5 s

s₂ = 0.5(2.5)

s₂ = 1.25 m.

Note: Distance between the pelican and fish = s₁ + s₂

Distance between the pelican and fish  = 29.41+1.25

Distance between the pelican and fish  = 30.66

Distance between the pelican and fish ≈ 31 m

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Answer and explanation:

A correct option is an option (B).

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Option (A) is incorrect because if charges are opposite, the value of force will not be zero. It will be -ve.

Option (C) is incorrect because the force is directly proportional to the product of charges, it depends on the amount of charge.

Option (D) is also incorrect because the force in inversly proportional to the distance between two charges. Thus, if the distance between two charges is increased, the force between two charges will decrease.

Concllusion:

The correct option is option (B).

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