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Minchanka [31]
2 years ago
12

A bicyclist travels $4.5\text{ km}$ west, then travels $6.7\text{ km}$ at an angle $27.0^\circ$ South of West.

Physics
1 answer:
MatroZZZ [7]2 years ago
7 0

Answer:

10.88 km

Explanation:

We shall represent displacement in terms of i , j  unit vectors in the direction of east and north .

4.5 km due west

D₁ = - 4.5 i

6.7 km at an angle of 27° south of west

D₂ = - 6.7 cos27 i - 6.7 sin27j

= - 6.7 x .89 i - 6.7 x .45 j

= - 5.96i - 3 j

Total displacement

= D₁ + D₂

=  - 4.5 i - 5.96i - 3 j

= -10.46 i - 3j

Magnitude = √ ( 10.46² + 3²)

= √ ( 109.41 + 9)

= √ 118.41

= 10.88 km .

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A 45 kg wagon is being pulled with a rope that makes an angle of 38 degrees with the horizontal. The applied force is 410 N and
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Answer:

7.35m/s²

Explanation:

From the question we are not told what to find but we can as well find the acceleration of the wagon.

According to newton second law of motion

\sum F_x = ma_x\\Fm - Ff = ma_x\\Fm - \mu R = ma_x\\Fm- \mu mg = ma_x\\

Fm is the moving force = 410N

\mu is the coefficient of friction = 0.18

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g is the acceleration dur to gravity = 9.8m/s²

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Substitute the given data into the equation ang get ax

Fm- \mu mg = ma_x\\410 - (0.18)(9.8)(45) = 45a_x\\410 - 79.38 = 45a_x\\330.62 = 45a_x\\a_x = 330.62/45\\a_x = 7.35m/s^2\\

Hence the acceleration of the wagon is 7.35m/s²

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