Question

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.)

Answer 1

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

Answer 2

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

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Further explanation

Vector is quantity that has magnitude and direction.

One example of a vector is displacement.

Let us now tackle the problem !

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This problem is about Vector Diagram.

Given:

distance between observer and intersection = y = 60 m

speed of cyclist = v = 10 m/s

elapsed time = t = 8 s

Asked:

speed of cyclist relative to observer = v' = ?

Solution:

Firstly , we will calculate the distance between the cyclist and intersection:

$x = v t$

$x = 10 \times 8$

$x = 80 \texttt{ m}$

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Next , we could calculate the speed of cyclist relative to observer:

$v' = v \times \cos \theta$

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

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

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

$v' = 8 \texttt{ m/s}$

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Conclusion :

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

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Learn more

• 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

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Answer details

Grade: High School

Subject: Physics

Chapter: Vectors