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nignag [31]
2 years ago
11

A cart is propelled over an xy plane with acceleration compo- nents ax 4.0 m/s2 and ay 2.0 m/s2. Its initial velocity has com- p

onents v0x 8.0 m/s and v0y 12 m/s. In unit-vector notation, what is the velocity of the cart when it reaches its greatest y coordinate?
Physics
1 answer:
Tasya [4]2 years ago
4 0

Answer:

(-16.0\ \hat i+0\ \hat j)\ \rm m/s.

Explanation:

<u>Given:</u>

  • x-component of acceleration of the cart, \rm a_x = 4.0\ m/s^2.
  • y-component of acceleration of the cart, \rm a_y = 2.0\ m/s^2.
  • x-component of initial velocity of the cart, \rm v_{0x} = 8.0\ m/s.
  • y-component of initial velocity of the cart, \rm v_{0y} = 12\ m/s.

Let the x and y components of the final velocity of the cart when the cart reaches its greatest y coordinate be \rm v_x\ and \ v_y respectively.

When the cart reaches its greatest y-coordinate then the y component of its final velocity should be zero, \rm v_y =0.\\

Let the cart reaches its greatest y-coordinate at time t, then using the following equation:

\rm v_y = v_{0y}+a_yt\\0=12+2\times t\\\Righttarrow t=\dfrac{-12}{2}=-6\ s.

At this time, the x component of the velocity of the particle is given by

\rm v_x = v_{0x}+a_xt=8.0+4.0\times (-6)=8.0-24.0=-16.0\ m/s.

Thus, the velocity of the cart when it reaches its greatest y coordinate, in unit-vector notation, is given by

\vec v = v_x\hat i+v_y\hat j=(-16.0\ \hat i+0\ \hat j)\ \rm m/s.

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A 5 kg wooden block sitson a flat straight-away12 meters fromthe bottom of an infinitely long ramp, which has an angle of 20 deg
saveliy_v [14]

Answer:

(a) 19.71801m/s Velocity just before going up the ramp.

(b) 74.56338m.

Explanation:

We will solve it in two parts, first we will calculate time that 5kg wooden block would take to just reach ramp and with this time we will calculate final velocity that the wooden block would have in this time.

Second, we will calculate the component of velocity vector along inclined plane and the time that it would take for velocity to be 0 meters/s then with this time we will calculate the distance that inclined plane would travel along inclined plane.

Following formulas will be used.

                                  x(t) = \frac{1}{2} t^2 = 12m =16.2m/s^2 t^2

                                 F =ma

                                 V(t) = V_{o} +at

                                 x(t) = x_{0} +v_{0}t+\frac{1}{2}a t^2

(a) Calculating velocity right before going up the ramp.

 Wooden block is going on a straightaway and has net for on it.

         F_{n} =F-F_{s} = F-uF_{n}  = 100N-0.4*9.8m/s^2*5kg =81N

     and this force produces acceleration of

      a = \frac{F}{m}=\frac{81}{5} =16.2m/s^2 .

With this acceleration, wooden block would reach at the foot of ramp in.

          x(t) = 12m = 16.2m/s^2*t^2

         t = 1.217s

and final velocity will be

v(t) = v_{0}+at = 0+16.2m/s^2*1.2171s = 19.7180m/s.

this velocity of wooden box just before going up the ramp.

(b) How far up the ramp will the wooden block go before stopping.

Ramp is at 20° relative to horizontal therefore velocity along the ramp that the wooden block would have will be.

                              V= V_{h}cos(20) = 18.5288m/s

and deceleration along the ramp is

                              a = \frac{F_{s} }{m}

 Where F_{s} force of friction along the inclined plane.

F_s =  uF_n = u*m*a

a = 9.8m/s^2*cos(20) = 9.2089m/s^2

is a component of g along normal of the inclined plane.

                               F_{s} = 0.25*5kg*9.2089m/s^2

                              = 11.5112N

                              a = \frac{11.5112N}{5kg} = 2.3022m/s^2

And with this deceleration time needed to get wooded block to stop is.

                     v(t) = v_o-at = 18.5288m/s-2.3022m/s^2*t = 0

                        t = \frac{18.5288m/s}{2.3022m/s^2} =8.04813s

 and in that time wooden block would travel

   x(8.04813s) = 18.52881m/s *8.04813s-\frac{1}{} 2.3022m/s^2*(8.0481)^2=74.56338m

This is how up wooden box will go before coming to stop.

3 0
3 years ago
Margy is trying to improve her cardio endurance by performing an exercise in which she alternates walking and running 100.0 m ea
Kipish [7]

Answer:

6.5 m/s

Explanation:

We are given that

Distance, s=100 m

Initial speed, u=1.4 m/s

Acceleration, a=0.20 m/s^2

We have to find the final velocity at the end of the 100.0 m.

We know that

v^2-u^2=2as

Using the formula

v^2-(1.4)^2=2\times 0.20\times 100

v^2-1.96=40

v^2=40+1.96

v^2=41.96

v=\sqrt{41.96}

v=6.5 m/s

Hence, her final velocity at the end of the 100.0 m=6.5 m/s

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What is radioactive dating? How is it used to determine age of something?
Liono4ka [1.6K]

Answer:

Technique of comparing abundance ratio between radioactive isotopes to a reference isotope to determine the age of a material called radioactive dating. It determines the age by having a more abundance of isotopes in the cellular being.

6 0
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Steel Usually forms a
meriva

Answer:

Permanent magnetism (of the steel)

make me brainliestt :))

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Coherent green light shines on a double slit with spacing 241um. This results in a diffraction pattern consisting of a central m
lilavasa [31]

Answer:

Becomes greater

Explanation:

Distance between the central maxima and the next line increase with the wavelength i.e.

d =\frac{3 \lambda L}{2a}

As, the wavelength of the red light is greater than the wavelength of the green light, thus, the distance between  the central maxima and the next line becomes greater.

Option 5 is correct.

4 0
3 years ago
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