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4 years ago

Given the displacement vector D = (2î − 6ĵ) m, find the displacement vector (in m) R so that D + R = −5Dĵ.

Physics

1 answer:

shusha [124]4 years ago

7 0

Answer:

R = (-2î − 6ĵ + 10k^)m

Explanation:

We are given;

D = (2î − 6ĵ)

Now, we want to find R such that,

D + R = −5Dĵ

Plugging in (2î − 6ĵ) for D in the R equation gives;

(2î − 6ĵ) + R = -5(2î − 6ĵ)j

(2î − 6ĵ) + R = -10k + 0

This is because in vector multiplication, i × j = k and j × j = 0

Thus;

(2î − 6ĵ) + R = -10k

Making R the subject gives;

R = -2î − 6ĵ + 10k^

Thus, the displacement vector R is;

R = (-2î − 6ĵ + 10k^)m

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#27 question

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So, the initial altitude of the parachuter is approximately <u>(C). 123 m</u>.

<h2>Introduction</h2>

Hi ! In this question, I will help you. In this question, you will learn about the fall time of the free fall motion. Free fall is a downward vertical motion without being preceded by an initial velocity. When moving in free fall, the following equations apply:

<h3>The equation for calculating the height (h)</h3>

$\boxed{\sf{\bold{h = \frac{1}{2} \cdot g \cdot t^2}}}$

<h3>The equation for calculating the time (s)</h3>

$\boxed{\sf{\bold{t = \sqrt{\frac{2 \cdot h}{g}}}}}$

<h3>The equation for calculating the velocity (v)</h3>

$\boxed{\sf{\bold{v = \sqrt{2 \times g \times h}}}}$

With the following condition :

t = interval of the time (s)
h = height or any other displacement at vertical line (m)
g = acceleration of the gravity (m/s²)
v = velocity (m/s)

<h2>Problem Solving</h2>

We know that :

t = interval of the time = 5 s
g = acceleration of the gravity = 9.81 m/s²

What was asked :

h = height or displacement at vertical line = ... m

Step by Step :

$\sf{h = \frac{1}{2} \cdot g \cdot t^2}$

$\sf{h = \frac{1}{2} \cdot 9.81 \cdot 5^2}$

$\sf{h = \frac{245.25}{2}}$

$\boxed{\sf{h = 122.625 \: m \approx 123 \: m}}$

<h3>Conclusion</h3>

So, the initial altitude of the parachuter is approximately 123 m (C.)

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