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melomori [17]
3 years ago
15

Two roads intersect at right angles, one going north-south, the other east-west. an observer stands on the road 60 meters south

of the intersection and watches a cyclist travelling east at 10 meters per second. at what rate is the cyclist moving away from the observer 8 seconds after he passes through the intersection? (hint: remember 3-4-5 rightangled triangles.)

Physics
2 answers:
Sloan [31]3 years ago
7 0

observer is standing at distance d = 60 m south from the intersection

cyclist is travelling at speed v = 10 m/s

now after t = 8 s its displacement from intersection is given by

x = 10*8 = 80 m

so the position of cyclist makes an angle with the observer

\theta = tan^{-1}\frac{80}{60} = 53 degree

now the component of velocity of cyclist along the line joining its position with the observer is given as

v = v_o cos\phi

here

\phi = 90 -\theta

\phi = 90 - 53 = 37 degree

v = 10 cos37 = 8 m/s

so at this instant cyclist is moving away with speed 8 m/s

Anna007 [38]3 years ago
3 0

The cyclist moving away from the observer 8 seconds after he passes through the intersection at the rate 8 m/s

\texttt{ }

<h3>Further explanation</h3>

Vector is quantity that has magnitude and direction.

One example of a vector is displacement.

Let us now tackle the problem !

\texttt{ }

This problem is about Vector Diagram.

<u>Given:</u>

distance between observer and intersection = y = 60 m

speed of cyclist = v = 10 m/s

elapsed time = t = 8 s

<u>Asked:</u>

speed of cyclist relative to observer = v' = ?

<u>Solution:</u>

<em>Firstly , we will calculate the distance between the cyclist and intersection:</em>

x = v t

x = 10 \times 8

x = 80 \texttt{ m}

\texttt{ }

<em>Next , we could calculate the speed of cyclist relative to observer:</em>

v' = v \times \cos \theta

v' = v \times \frac{ x }{\sqrt{x ^2 + y^2}}

v' = 10 \times \frac { 80 }{\sqrt{80^2 + 60^2}}

v' = 10 \times \frac {4}{5}

v' = 8 \texttt{ m/s}

\texttt{ }

<h3>Conclusion :</h3>

The cyclist moving away from the observer 8 seconds after he passes through the intersection at the rate 8 m/s

\texttt{ }

<h3>Learn more</h3>
  • Direction of Displacement : https://brainly.ph/question/1746541
  • Scalar and Vector : https://brainly.ph/question/274572
  • Weight : https://brainly.ph/question/545327
  • Orientation of Vectors : https://brainly.ph/question/2121753

\texttt{ }

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Vectors

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         x = v₀ cos 43 t

         x = 32.64 cos 43  2.50

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