Two forces, F, = (-4.00î – 3.95j) N and F, = (-3.95î - 4.95j) N, act on a particle of mass 1.90 kg that is initially at rest at 1 coordinates (+1.95 m, +4.05 m). (a) What are the components of the particle's velocity at t = 11.1 s? m/s (b) In what direction is the particle moving at t = 11.1 s? ° counterclockwise from the +x-axis (c) What displacement does the particle undergo during the first 11.1 s? AF = m (d) What are the coordinates of the particle at t = 11.1 s? y = m

Two forces, F, = (-4.00î – 3.95j) N and F, = (-3.95î - 4.95j) N, act on a particle of mass 1.90 kg that is initially at rest at 1 coordinates (+1.95 m, +4.05 m). (a) What are the components of the particle's velocity at t = 11.1 s? m/s (b) In what direction is the particle moving at t = 11.1 s? ° counterclockwise from the +x-axis (c) What displacement does the particle undergo during the first 11.1 s? AF = m (d) What are the coordinates of the particle at t = 11.1 s? y = m

Related questions

Q: Sue gets up on the roof to clean off the leaf litter. Upon trying to get back down the ladder, she…

Q: - A stationary 1.83-kg potato is struck by a stick, delivering a horizontal force of F(t) = at — bt²…

Q: The only force acting on a 1.1 kg body as it moves along the positive x axis has an x component Fx =…

Q: You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors…

Q: what is the magnitude of the vertical acceleration of Ariane 5, in ?/?^2. Consider ?=9.8 ?/?^2…

A: During takeoff, the two-facet tank and critical tank exert a pressure at the earth, By newton's…

Q: Two forces, F, (5.80l + 3.955) N and F,- (3.90i + 7.65j) N, act on a particle of mass 1.90 kg that…

Q: 3. You wake up one morning to find yourself in a strange room with opaque walls, and no visible…

A: Given data: Initial velocity (Vi) = 0 m/s Mass (m) = 75.8 kg Height (h) = 1.10 m Time (t) = 0.331 s…

Q: velocity of the body at x = 4.2 m?

A: Given: Mass of body is m=3.5 kg Horizontal force on body is Fx=-8x N; here x is in meters. Velocity…

Q: A particle of mass 1.06 kg begins at rest and is then subject to a force in the positive x direction…

Q: For its size, the common flea is one of the most accomplished jumpers in the animal world. A…

Q: A time-dependent force, F = (7.90î - 3.30tj), where F is in newtons and t is in seconds, is exerted…

Q: You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors…

A: Given data: Mass (m) = 77.9 kg Initial velocity (Vi) = 0 m/s Height (h) = 1.79 m Time (t) = 0.302 s…

Q: An object with a mass of 1.93 kg is initially at rest upon a horizontal, frictionless surface. An…

A: Given data: Mass of an object is, m= 1.93 kg The object is initially at rest, vi = 0 The applied…

Q: A 60 g bullet with an initial speed of 700 m/s is fired parallel to a ramp at an angle 20° into a…

Q: A spring that has negligible mass and a spring constant of k = 900 N/m, is attached to a table, so…

A: We are given the initial compression in the spring. We are also given the spring constant. When the…

Q: You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors…

A: Mass of the body (m) = 75.1 kg Height (h) = 1.38 m Time (t) = 0.424 sec

Q: A 8.7-kg cat moves from rest at the origin to hunk of cheese located 9.5 m along the x-axis while…

Q: You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors…

A: Given Mass of the person is m=63.1 kg Height from where the object is dropped is h=2.05 m Time taken…

Q: kinetic energy

Q: Two masses move along the frictionless x-axis. m₁=13.7kg is initially moving with a velocity v₁ = m₂…

A: Given,The masses, The velocity of both masses,The momentum of masses before collision,The momentum…

Q: You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors…

A: 1850 NExplanation:

Q: Tarzan 70 kg frantically running from a wild boar, grabs a vine hanging vertically and swings out of…

Q: A mass M1 (of 2.5 kg) slides without friction on a table at a speed of 5 m/sec towards a mass M2 of…

A: M1 = 2.5 kg v = 5 m/s M2 = 5 kg k = 100 N/m

Q: Two forces, F1 = (6.10î + 4.30ĵ) N and F2 = (3.40î + 7.65ĵ) N, act on a particle of mass 2.20 kg…

Q: A ball of mass 160 g is dropped from a height 1.5 m and bounces off the floor with a velocity 3.0…

A: Mass of ball is Initial height is Velocity of ball after bouncing from the floor is in upward…

Q: Two forces, 1 = (−6.55î + 4.75ĵ) N and 2 = (−4.05î + 6.40ĵ) N, act on a particle of mass 2.20 kg…

Q: You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors…

A: Given that: m=66.5 kgh=1.02 mu=0t=0.274 seca=?

Q: I am driving down the street at 23.4 mi/h and suddenly I see a squirrel. I slam on the brakes in…

A: Given that: Speed of car, u = 23.4 mi/h = 23.4 X 1.60 = 37.44 km/h= 10.4 m/s Time of decleration, t…

Q: kinetic energy of the projectile in kilojoules

Q: The mass of particle 1 is 12.9kg, and its initial velocity is v_1i = (27m/s)i + (3m/s)j.…

Q: A stationary 1.57-kg potato is struck by a stick, delivering a horizontal force of F(t) = at — bt²…

Q: A cart of mass m₁ = 4 kg is on frictionless surface and compressed against an ideal spring with…

A: Let the velocity of first cart before hitting the second cart be v. Since this velocity is a result…

Q: You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors…

Question

Two forces, F
:(-4.00î – 3.95ĵ) N and F, = (-3.95î – 4.95j) N, act on a particle of mass 1.90 kg that is initially at rest at
1
coordinates (+1.95 m, +4.05 m).
(a) What are the components of the particle's velocity at t = 11.1 s?
m/s
(b) In what direction is the particle moving at t = 11.1 s?
° counterclockwise from the +x-axis
(c) What displacement does the particle undergo during the first 11.1 s?
(d) What are the coordinates of the particle at t = 11.1 s?
X =
m
y =

Expert Solution

Step 1

Solution:

Given

$\overset{⇀}{F_{1}} = (- 4.00 \overset{⏜}{i} - 3.95 \overset{⏜}{j}) N \overset{⇀}{F_{2}} = (- 3.95 \overset{⏜}{i} - 4.95 \overset{⏜}{j}) N mass m = 1.90 kg coordinates = (+ 1.95 m + 4.05 m)$

(a) Net force on the particle is

$\overset{⇀}{F} = \overset{⇀}{F_{1}} + \overset{⇀}{F_{2}}$

$\overset{⇀}{F} = (- 4 \overset{⏜}{i} - 3.95 \overset{⏜}{j}) + (- 3.95 \overset{⏜}{i} - 4.95 \overset{⏜}{j}) \overset{⇀}{F} = (- 7.95 \overset{⏜}{i} - 8.9 \overset{⏜}{j}) N$

we know that

acceleration= $\overset{⇀}{a} = \frac{\overset{⇀}{F}}{m} = \frac{(- 7.95 \overset{⏜}{i} - 8.9 \overset{⏜}{j}) N}{1.90 kg}$

$∴ \overset{⇀}{a} = (- 4.18 \overset{⏜}{i} - 4.68 \overset{⏜}{j}) m / s^{2}$

So,

$\overset{⇀}{v} = \overset{⇀}{u} + \overset{⇀}{at} \overset{⇀}{v} = 0 + (- 4.18 \overset{⏜}{i} - 4.68 \overset{⏜}{j}) m / s^{2} (11.1 s) \overset{⇀}{v} = (- 46.39 \overset{⏜}{i} - 51.94 \overset{⏜}{j}) m / s$

x-component = -46.39 m/s

y-component = -51.94 m/s

Therefore,

The components of the particle's velocity at t=11.1 S is

$\overset{⇀}{v} = (- 46.39 \overset{⏜}{i} - 51.94 \overset{⏜}{j}) m / s$

(b)

We know that

$tanθ = \frac{v_{y}}{v_{x}}$

$\tan θ = \frac{- 51.94}{- 46.39} = 1.11 θ = \tan^{- 1} (1.11) ∴ θ = 47 . 98^{o}$

Hence,

The particle is moving at an angle $θ = 47 . 98^{o}$

counter clockwise from the +x-axis.

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

A block having a mass of 1.0 kg is given an initial velocity v= 6 m/s to the right and collides with a spring whose mass is negligible and whose force constant is k =100 N/m . Assuming the surface to be frictionless, e the maximum compression of the spring after the collision m 6 m 5 m None
The only force acting on a 4.5 kg body as it moves along the positive x axis has an x component Fx = -6x N, where x is in meters. The velocity of the body at x = 1.9 m is 8.2 m/s. (a) What is the velocity of the body at x = 4.5 m? (b) At what positive value of x will the body have a velocity of 5.9 m/s?
Where necessary assume g = 9.8 m s-² 1. A vehicle has a mass of 1800 kg. Its engine provides a forward force of 2.5 kN, but the motion is resisted by a constant frictional force of 340 N. Calculate a) the acceleration of the vehicle, b) its momentum 6.0 s after starting to move.
You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors or windows. You decide to do some experiments to find out more about your strange situation. Your own body mass is 50.1 kg. You pick up an object and drop it from rest, starting at a height of 1.97 meters above the floor, and it hits the floor 0.380 seconds later. You can ignore air resistance. Based on the outcome of this experiment, when you step on the scale provided for you, what weight will it register for your body? 684 N 911 N 1,367 N 491.5 N
The only force acting on a 3.6 kg body as it moves along the positive x axis has an x component Fx = - 5x N, where x is in meters. The velocity of the body at x = 1.8 m is 9.0 m/s. (a) What is the velocity of the body at x = 4.1 m? (b) At what positive value of x will the body have a velocity of 2.5 m/s?
You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors or windows. You decide to do some experiments to find out more about your strange situation. Your own body mass is 53.3 kg. You pick up an object and drop it from rest, starting at a height of 2.40 meters above the floor, and it hits the floor 0.560 seconds later. You can ignore air resistance. Based on the outcome of this experiment, when you step on the scale provided for you, what weight will it register for your body? 544 N 816 N 522.9 N 408 N
You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors or windows. You decide to do some experiments to find out more about your strange situation. Your own body mass is 56.0 kg. You pick up an object and drop it from rest, starting at a height of 2.35 meters above the floor, and it hits the floor 0.346 seconds later. You can ignore air resistance. Based on the outcome of this experiment, when you step on the scale provided for you, what weight will it register for your body? 549.4 N 1,100 N 1,466 N 2,199 N
You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors or windows. You decide to do some experiments to find out more about your strange situation. Your own body mass is 72.3 kg. You pick up an object and drop it from rest, starting at a height of 1.52 meters above the floor, and it hits the floor 0.223 seconds later. You can ignore air resistance. Based on the outcome of this experiment, when you step on the scale provided for you, what weight will it register for your body? 1 2,210 N 2 2,947 N 3 4,420 N 4 709.3 N
A horizontal force of 80.0 N is applied to a 5.00 kg block as the block slides a distance of 0.800 m along a horizontal floor. The coefficient of kinetic friction between the floor and the block is 0.500. If the block is initially at rest, how fast is it moving at the end of the displacement?
You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors or windows. You decide to do some experiments to find out more about your strange situation. Your own body mass is 71.1 kg. You pick up an object and drop it from rest, starting at a height of 1.82 meters above the floor, and it hits the floor 0.305 seconds later. You can ignore air resistance. Based on the outcome of this experiment, when you step on the scale provided for you, what weight will it register for your body? 1,391 N 1,855 N 2,782 N 697.5 N
The only force acting on a 4.2 kg body as it moves along the positive x axis has an x component Fx= -4x N, where x is in meters. The velocity of the body at x = 1.7 m is 8.1 m/s. (a) What is the velocity of the body at x = 3.9 m? (b) At what positive value of x will the body have a velocity of 2.3 m/s? (a) Number i Units (b) Number i Units
You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors or windows. You decide to do some experiments to find out more about your strange situation. Your own body mass is 54.7 kg. You pick up an object and drop it from rest, starting at a height of 1.20 meters above the floor, and it hits the floor 0.396 seconds later. You can ignore air resistance. Based on the outcome of this experiment, when you step on the scale provided for you, what weight will it register for your body?