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
-Dominant- [34]
2 years ago
13

The kittens, Annie and Josie, are pushing a ball, Annie with a force magnitude of 80 N in a direction of 133 degrees, and Josie

with a magnitude of 95 N in a direction of 290 degrees. If a third cat wants to prevent the ball from moving, with what magnitude and direction of force must she push?
Mathematics
1 answer:
kvv77 [185]2 years ago
7 0

Answer: Then the magnitude of the force is 37.86N, and the direction is 54.35°

Step-by-step explanation:

We can write the forces as vectors.

We know that Annie pushes with a magnitude of 80N in a direction of 133° (Remember that the angles are always measured from the x-axis)

The components of this force, (Ax, Ay), are then:

Ax = 80N*cos(133°)

Ay = 80N*sin(133°)

And we know that Josie pushes with a magnitude of 95N in direction of 290°

The components of this force, (Jx, Jy), are:

Jx = 95N*cos(290°)

Jy = 95N*sin(290°)

When we add these forces, the total force acting on the ball is:

F = (80N*cos(133°) ,  80N*sin(133°)) + (95N*cos(290°), 95N*sin(290°))

F = (80N*cos(133°) + 95N*cos(290°), 80N*sin(133°) + 95N*sin(290°))

Now, the third kitten wants to do a force K, in a direction θ, such that the net force acting on the ball is zero.

Then we must have that, each component of the force of the third cat (K*cos(θ)  on the x-axis and k*sin(θ) on the y-axis), is such that:

K*cos(θ) + 80N*cos(133°) + 95N*cos(290°) = 0

k*sin(θ)  + 80N*sin(133°) + 95N*sin(290°) = 0

Now we need to solve that system for k and θ

if we simplify the equations we get:

k*cos(θ) - 22.07N = 0

k*sin(θ)  -30.76N  = 0

Now we can rewrite them as:

k*cos(θ) = 22.07N

k*sin(θ)   = 30.76N  

Now we can take the quotiet between both equations to get:

(k*sin(θ))/(k*cos(θ)) = 30.76N/22.07N

Tan(θ) = 1.394

θ = Atan(1.394) = 54.35°

Now that we know the angle, we can find the value of the magnitude k, by using one of the two equations of the system:

k*cos(54.35°) = 22.07N

k = 22.07N/cos(54.35°) = 37.86N

Then the magnitude of this force is 37.86N, and the direction is 54.35°

You might be interested in
[100 POINTS] What is the measure of the arc from A to B that does not pass through C?
prohojiy [21]

Answer:

the answer to the questions is 140

5 0
1 year ago
Read 2 more answers
John has all the marbles in the world. What percent of the worlds marbles does John have?
Eddi Din [679]

Answer:

100%

Step-by-step explanation:

All of them = 100%.

7 0
3 years ago
If your good in geometry answer !!
kati45 [8]
Oof that a hard one
4 0
3 years ago
Write your answer in simplest radical form​
devlian [24]
I believe the correct answer is 8sqrt2.
3 0
2 years ago
Two angles are vertical angles. One is labeled 2x. The other angle is labeled (x+30). Find the value of x.
NeX [460]

2x=x+30

-x    -x

x=30

The value of x is 30

5 0
3 years ago
Other questions:
  • What is the answer too this,it’s rational numbers - 3.3(6)= ?
    11·2 answers
  • Ive been stuck on this question for 4 hours someone please help me
    7·1 answer
  • An account earned $143.86 in simple interest over 4 years and 3 months. There were no deposits or withdraws on the account. The
    13·1 answer
  • Train A leaves the station traveling east at 55 mph, while train B leaves the station 45 minutes later traveling west at 70 mph.
    8·1 answer
  • A number multiplied by 4 is -20
    10·2 answers
  • What is 271,000 rounded tothe nearest hunded thousand
    15·2 answers
  • Find the next three terms of the geometric sequence -8, 12, -18,27
    8·1 answer
  • Selena walks from home to school each morning and back home each afternoon altogether she walks to 3/2miles each day how far is
    14·1 answer
  • Which statement best explains why the Exodus is an important event in the Jewish religion?
    5·1 answer
  • Can Someone Help? Im already failing Math Badly
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!