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3 years ago

A vector is 9.55m long and points in a -48.0 degree direction. find the x component

Physics

1 answer:

stich3 [128]3 years ago

8 0

Answer:

Explanation:

<u>Rectangular Components of a Vector</u>

Vectors can be expressed in several forms, including the magnitude-angle form, and the rectangular-coordinates form.

If the magnitude r and angle β are given, we can find the rectangular coordinates (x,y) as follows:

$x=r\cos\beta$

$y=r\sin\beta$

The vector of the question has a magnitude of r=9.55 m and an angle β=-48°. The x-component is:

$x=9.55\cdot\cos(-48^\circ)$

Using a digital calculator:

x=6.39 m

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Question:

A 63.0 kg sprinter starts a race with an acceleration of 4.20m/s square. What is the net external force on him? If the sprinter from the previous problem accelerates at that rate for 20m, and then maintains that velocity for the remainder for the 100-m dash, what will be his time for the race?

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Given data:

As the sprinter starts the race so initial velocity = v₁ = 0

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Distance = s₂ = 100 m

We first need to find the final velocity (v₂) of sprinter at the end of the first 20 meters.

Using 3rd equation of motion

(v₂)² - (v₁)² = 2as₁ = 2(4.2)(20)

v₂ = 12.96 ms⁻¹

Time for 20 m distance = t₁ = (v₂ - v ₁)/a

t₁ = 12.96/4.2 = 3.09 s

He ran the rest of the race at this velocity (12.96 m/s). Since has had already covered 20 meters, he has to cover 80 meters more to complete the 100 meter dash. So the time required to cover the 80 meters will be

Time for 100 m distance = t₂ = s₂/v₂

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3 years ago

A vector is 9.55m long and points in a -48.0 degree direction. find the x component​

A vector is 9.55m long and points in a -48.0 degree direction. find the x component