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pickupchik [31]
2 years ago
11

Julianne went to a restaurant to have a taste of her favorite fried chicken and spaghetti. She drove 2 km, east and then 8.5 km,

northeast. What is Julianne’s displacement from her origin?
Physics
1 answer:
GREYUIT [131]2 years ago
5 0

Julianne’s displacement from her origin is equal to 10.015 kilometers.

<u>Given the following data:</u>

  • Distance A = 2 km, East.
  • Distance B = 8.5 km, Northeast.

To calculate Julianne’s displacement from her origin:

<h3>How to calculate displacement.</h3>

We would denote the two (2) unit vectors along the East and Northeast directions by i and j respectively.

<u>Note:</u> Northeast is at angle of 45° with the East.

In terms of vectors, the distances becomes:

Distance A = 2i

Distance\;B=8.5 [(cos 45i + sin 45j)]\\\\Distance\;B=(\frac{8.5}{\sqrt{2} } i \;+\;\frac{8.5}{\sqrt{2} } j)

<u>For the </u><u>resultant displacement</u><u>:</u>

D^2 = [(2+\frac{8.5}{\sqrt{2} } )^2+ (\frac{8.5}{\sqrt{2} } )^2\\\\D =\sqrt{[(2+\frac{8.5}{\sqrt{2} } )^2+ (\frac{8.5}{\sqrt{2} } )^2} \\\\D=2+\frac{8.5}{\sqrt{2} } + \frac{8.5}{\sqrt{2} }

D = 10.015 kilometers.

Read more on displacement here: brainly.com/question/13416288

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A motorcyclist heading east through a small town accelerate at constant 4.0meter per seconds square after he leaves the limits.
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A) The position at t = 2.0 sec is 43.0 m east

B) The position is 55 m east

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A)

In order to solve the problem, we take the east direction as positive direction.

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- at t = 0, the initial velocity of the motorcyclist is v_0 = 15.0 m east

- The acceleration of the motorcyclist is constant and it is a=4.0 m/s^2

Since the motion is a uniformly accelerated motion, the position of the motorcylist is given by the expression

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Substituting t = 2.0 s, we find the position:

x(2.0)=(5.0)+(15)(2.0)+\frac{1}{2}(4.0)(2.0)^2=43 m

B)

The velocity of the motoryclist can be found by calculating the derivative of the position. Therefore, it is:

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Solving the equation for t,

t=\frac{v-v_0}{a}=\frac{25-15}{4}=2.5 s

And therefore, the position at t = 2.5 s is:

x(2.5s)=5.0+(15.0)(2.5)+\frac{1}{2}(4)(2.5)^2=55 m

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