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3 years ago

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A fly enters through an open window and zooms around the room. In a Cartesian coordinate system with three axes along three edge

s of the room, the fly changes its position from point b (2.5 m, 2.0 m, 4.0 m) to point e (4.5 m, 3.0 m, 3.5 m). Find the scalar components of the flies displacement vector (in m).

1 answer:

AnnyKZ [126]3 years ago

7 0

Answer:

Explanation:

Displacement vector along x axes = 4.5 - 2.5 = 2 m

Displacement vector along y axes = 3 - 2 = 1 m

Displacement vector along z axis = 3.5- 4 = - 0.5 m

Displacement vector = 2 i + j - 0.5 k m

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What would happen to the planets in the solar system if the sun’s gravitational force were to suddenly disappear?

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3 years ago

Read 2 more answers

Express 79 m in units of (a) centimeters

dem82 [27]

Answer: a) 7,00 centimeters

(b) 259. 19 feet

(c) 3110.28 inches

(d) 0.049 miles

Explanation:

(a) We know that 1 meter = 100 centimeters

Therefore,

$79\ m= 7,900\text{ centimeters}$

(b)Since 1 meter = 3.28084 feet

Then, $79\ m= 79\times3.28084=259.18636\approx 259.19\text{ feet}$

(c) Since, 1 feet = 12 inches.

$79\ m=259.19\text{ feet}=259.19\times12=3110.28\text{ inches}$

(d) $\text{Since 1 feet= }\dfrac{1}{5280}\text{ mile}$

$79\ m=259.19\text{ feet}=\dfrac{259.19}{5280}= 0.0490890151515\approx0.049\text{ miles}$

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3 years ago

A turtle and a rabbit are in a 150 meter race. The rabbit decides to give the turtle a 1 minute head start. The turtle moves at

yan [13]

Answer:

a) $s_{T} = 30\,m$ , b) $t = 5\,min$ , c) $\Delta t = 6.667\,s$ , d) $\Delta s_{R} = 33.333\,m$ , e) $t' = 11.667\,s$ , f) The rabbit won the race.

Explanation:

a) As turtle moves at constant speed, its position is determined by the following formula:

$s_{T} = v_{T}\cdot t$

Where:

$t$ - Time, measured in seconds.

$v_{T}$ - Velocity of the turtle, measured in meters per second.

$s_{T}$ - Position of the turtle, measured in meters.

Then, the position of the turtle when the rabbit starts to run is:

$s_{T} = \left(0.5\,\frac{m}{s} \right)\cdot (60\,s)$

$s_{T} = 30\,m$

The position of the turtle when the rabbit starts to run is 30 meters.

b) The time needed for the turtle to finish the race is:

$t = \frac{s_{T}}{v_{T}}$

$t = \frac{150\,m}{0.5\,\frac{m}{s} }$

$t = 300\,s$

$t = 5\,min$

The time needed for the turtle to finish the race is 5 minutes.

c) As rabbit experiments a constant acceleration until maximum velocity is reached and moves at constant speed afterwards, the time required to reach such speed is:

$v_{R} = v_{o,R} + a_{R}\cdot \Delta t$

Where:

$v_{R}$ - Final velocity of the rabbit, measured in meters per second.

$v_{o,R}$ - Initial velocity of the rabbit, measured in meters per second.

$a_{R}$ - Acceleration of the rabbit, measured in $\frac{m}{s^{2}}$ .

$\Delta t$ - Running time, measured in second.

$\Delta t = \frac{v_{R}-v_{o,R}}{a_{R}}$

$\Delta t = \frac{10\,\frac{m}{s}-0\,\frac{m}{s}}{1.50\,\frac{m}{s^{2}} }$

$\Delta t = 6.667\,s$

The time taken by the rabbit to reach maximum speed is 6.667 s.

d) On the other hand, the position reached by the rabbit when maximum speed is reached is determined by the following equation of motion:

$v_{R}^{2} = v_{o,R}^{2} + 2\cdot a_{R}\cdot \Delta s_{R}$

$\Delta s_{R} = \frac{v_{R}^{2}-v_{o,R}^{2}}{2\cdot a_{R}}$

$\Delta s_{R} = \frac{v_{R}^{2}-v_{o,R}^{2}}{2\cdot a_{R}}$

Where $\Delta s_{R}$ is the travelled distance of the rabbit from rest to maximum speed.

$\Delta s_{R} = \frac{\left(10\,\frac{m}{s} \right)^{2}-\left(0\,\frac{m}{s} \right)^{2}}{2\cdot \left(1.50\,\frac{m}{s^{2}} \right)}$

$\Delta s_{R} = 33.333\,m$

The distance travelled by the rabbit from rest to maximum speed is 33.333 meters.

e) The time required for the rabbit to finish the race can be determined by the following expression:

$t' = \frac{\Delta s_{R}}{v_{R}}$

$t' = \frac{150\,m-33.333\,m}{10\,\frac{m}{s} }$

$t' = 11.667\,s$

The time required for the rabbit from rest to maximum speed is 11.667 seconds.

f) The animal with the lowest time wins the race. Now, each running time is determined:

Turtle:

$t_{T} = 300\,s$

Rabbit:

$t_{R} = 60\,s + 6.667\,s + 11.667\,s$

$t_{R} = 78.334\,s$

The rabbit won the race as $t_{R} < t_{T}$ .

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3 years ago

Consider the possible scenarios and determine which of them are true for positive feedbacks or negative feedbacks.A. Increased p

avanturin [10]

Answer:

Scenario A, B and E is True.

Explanation:

Scenario A) True. Removing carbon dioxide from atmosphere decreases greenhouse effect of atmosphere. Thus, temperature rise decreases.

Scenario B) True. The more evaporation creates the more greenhouse effect. Therefore, temperature rise increases.

Scenario C) False. Removing carbon dioxide from atmosphere decreases greenhouse effect of atmosphere. Thus, temperature rise decreases.

Scenario D) False. The more evaporation creates the more greenhouse effect. Therefore, temperature rise increases.

Scenario E) True. If reflected radiation increases from Earth, temperature rise of the Earth will decrease. Ice cover increases reflectivity which leads temperature level decrease.

Scenario F) False. If reflected radiation increases from Earth, temperature rise of the Earth will decrease. Ice cover increases reflectivity which leads temperature level decrease.

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3 years ago