1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dmitriy555 [2]
3 years ago
12

A small particle starts from rest from the origin of an xy-coordinate system and travels in the xy-plane. Its acceleration in th

e x-direction is 2m/s^2, and its acceleration in the y-direction is 1m/s^2. What is the x-coordinate of the particle when the y-coordinate is 12m?
Physics
2 answers:
Oduvanchick [21]3 years ago
8 0
<h2>Answer:</h2>

24m

<h2>Explanation:</h2>

Consider one of the equations of motion as follows;

s = ut + \frac{1}{2}at²            ----------------------------(i)

Where;

s = vertical/horizontal displacement of the body in motion

u = initial vertical/horizontal displacement of the body

t = time taken for the displacement

a = vertical/horizontal acceleration of the body.

Now, since the particle being considered moves in an xy-coordinate system, then equation (i) above can be resolved into the x (horizontal) and y (vertical) components as follows;

<u>Horizontal (x-coordinate) component</u>

s_{x} = u_{x} t + \frac{1}{2} a_{x}t²     ------------------(ii)

Where;

s_{x} = horizontal displacement (x-coordinate) of the particle in motion

u_{x} = initial horizontal displacement of the particle

t = time taken for the displacement

a_{x} = horizontal (x-direction) acceleration of the body.

<u>Vertical (y-coordinate) component</u>

s_{y} = u_{y} t + \frac{1}{2} a_{y}t²      -------------------(iii)

Where;

s_{y} = vertical displacement (y-coordinate) of the particle in motion

u_{y} = initial vertical displacement of the particle

t = time taken for the displacement

a_{y} = vertical (y-direction) acceleration of the body.

(A) Now, using equation (iii), from the question;

u_{y} = 0              [since the particle starts from rest, initial velocity is zero]

a_{y} = 1m/s²        [acceleration in the y-direction]

s_{y} = 12m           [y-coordinate value]

<em>Substitute these values into equation (iii) as follows;</em>

12 = 0 t +  \frac{1}{2} (1) t²

12 =   \frac{1}{2} t²          [Multiply through by 2]

24 = t²              [Solve for t]

t = \sqrt{24} seconds

(B) Also, using equation (ii), from the question;

u_{x} = 0              [since the particle starts from rest, initial velocity is zero]

a_{x} = 2m/s²       [acceleration in the x-direction]

s_{x} = ?               [x-coordinate value]

<em>Substitute these values into equation (ii) as follows;</em>

s_{x} = 0 t +  \frac{1}{2} (2) t²

s_{x} =  t²             -------------------(iv)

But t = \sqrt{24} seconds as calculated above, substitute this value into equation (iv)

s_{x} = (\sqrt{24})²              [Solve for s_{x}]

s_{x} = 24

Therefore, the x-coordinate of the particle when the y-coordinate is 12m is 24m

Gennadij [26K]3 years ago
4 0

Answer:

When the y-coordinate is 12m, the x-coordinate of the particle is 24 m

Explanation:

Given;

y - component of acceleration = 1 m/s²

X - component of acceleration = 2 m/s²

distance traveled in y - direction, Dy = 12 m

To determine the distance traveled in X- direction, we obtain the duration of the displacement in y- direction.

Applying equation of motion;

Dy = ¹/₂ x at²

t = \sqrt{\frac{2y}{a}} = \sqrt{\frac{2*12}{1}} = 4.9 s

For distance traveled in x -direction;

Dx = ¹/₂ x at²

Dx = ¹/₂ x 2 x (4.9)² = 24.01 m ≅ 24m

Therefore, when the y-coordinate is 12m, the x-coordinate of the particle is 24 m

You might be interested in
Which of these people have a stressed induced stomachache
castortr0y [4]
Molly & Caden have a stressed
4 0
3 years ago
Match up the following set of words with their definitions.
shepuryov [24]

Answer:

  1. weight
  2. mass
  3. force
  4. magnitude
  5. vector
  6. net force
7 0
2 years ago
How to do it? Urgent ​
mixer [17]

a)

F= ma

a=v/t

F=5*(35/5)

F=35N

b)

a=F/m

a=(35-2)/5

a=33/5

a=6.6N

8 0
3 years ago
2. A can filled with sand has a mass of 0.65kg is swung overhead in a horizontal circle of radius 0.70m at a constant rate of 2.
Aliun [14]
<h3><u>Answer</u>;</h3>

≈ 5 Kgm²/sec

<h3><u>Explanation</u>;</h3>

Angular momentum is given by the formula

L = Iω, where I is the moment of inertia and ω is the angular speed.

I = mr², where m is the mass and r is the radius

 = 0.65 × 0.7²

 = 0.3185

Angular speed, ω = v/r

                              = (2 × 3.142 × r × 2.5) r

                              =  15.71

Therefore;

Angular momentum =  Iω

                                 = 0.3185 × 15.71

                                 = 5.003635

                                 <u>≈ 5 Kgm²/sec</u>

6 0
3 years ago
A falcon can descend with a speed 250 km/h. If a falcon flies at this speed for 2.0 s and then flies a 100 m in 2.5 s, what is t
Vadim26 [7]

Answer:

v= s/t

Explanation:

250 km/ h =69.44m/s

S1=2 times 69.44 ≈ 139m

Next 2.5 seconds:

S2 = 100m

Average speed:

v=139m+100m/2s+2.5s = 239/4.5s = 53.2 m/s=192km/h

3 0
2 years ago
Other questions:
  • You ride your bike at 12.1 m/s directly away from your neighbor's trumpet sound and toward the sound of another neighbor's tromb
    6·1 answer
  • One of the world trade center towers WTC1 is 1,368 feet tall, what is it's height in meters?​
    10·1 answer
  • Technician A says that many bearings also have a thin overlay of babbitt. Technician B says that bearings should have spread and
    14·1 answer
  • What is a good question for a Science Fair (7th grade advanced) also im an online student so nothing really physical something t
    10·1 answer
  • The water in a deep underground well is used as the cold resevoir of a Carnot heat pump that maintains the temperature of a hous
    11·1 answer
  • How is an image produced by a plane mirror different than an image produced by a convex mirror
    14·2 answers
  • What part of an atom is involved in electricity and magnetism?*
    15·2 answers
  • Actiong-reaction of the bat hits the ball.
    10·1 answer
  • Which transformation will map figure L onto figure L'? (1 point) Two congruent triangles Figure L and Figure L prime are drawn o
    15·1 answer
  • Nancy ran a distance of 5km in 30 minutes. What is her speed in meters(m) per hour)h)
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!