Juana and Diego Gonzales, ages six and four respectively, own a strong and stubborn puppy named Corporal. It is so hard to take Corporal for a walk that they devise a scheme to use two leashes. If Juana pulls with a force of 23 lbs at an angle of 18° and Diego pulls with a force of 27 lbs at an angle of -15°, how hard is Corporal pulling if the puppy holds the children at a standstill?

Question

Juana and Diego Gonzales, ages six and four respectively, own a strong and stubborn puppy named Corporal. It is so hard to take Corporal for a walk that they devise a scheme to use two leashes. If Juana pulls with a force of 23 lbs at an angle of 18° and Diego pulls with a force of 27 lbs at an angle of -15°, how hard is Corporal pulling if the puppy holds the children at a standstill?

Im trying to figure out how to set this up?

Answer 1

let AP be the vector of magnitude 23 lbs and direction 18°

and BP be the vector of magnitude 27 lbs and direction -15°

Complete the parallogram APBQ , with
AP=2
BP=27
angle P = 33°
then angle B = 180-33 = 147°
So PQ is the force pulling by the puppy to hold the kids

In triangle BPQ
BP=27
BQ=23
angle B=147
PQ^2 = 23^2 + 27^2 - 2(23)(27)cos147
PQ^2 = 2299.628...
PQ = √...
= 47.95 lbs

Answer 2

To set up this problem, you can use vector addition to find the net force experienced by Corporal when Juana and Diego pull at different angles with different forces.

1. Convert the forces into horizontal and vertical components. To do this, you'll use trigonometry:

Juana's force:
Horizontal component (Fx1) = 23 lbs * cos(18°)
Vertical component (Fy1) = 23 lbs * sin(18°)

Diego's Force:
Horizontal component (Fx2) = 27 lbs * cos(-15°)
Vertical component (Fy2) = 27 lbs * sin(-15°)

Note: To find the horizontal component, use the cosine function, and for the vertical component, use the sine function. Be careful with the signs when calculating the components based on the angle.

2. Add the horizontal and vertical components separately to find the net force:

Horizontal net force (Fnetx) = Fx1 + Fx2
Vertical net force (Fnety) = Fy1 + Fy2

3. Calculate the magnitude of the net force using the Pythagorean theorem:

Net force magnitude (Fnet) = √(Fnetx^2 + Fnety^2)

The magnitude of the net force is the pull force applied by Corporal to keep the children at a standstill.

By following these steps, you can set up the problem and find the answer to how hard Corporal is pulling.

Answer 3

To set up this problem, we can use vector addition to find the net force acting on Corporal.

Step 1: Convert the forces into their respective x and y components.
Juana's force (Fj) has a magnitude of 23 lbs and an angle of 18°:
Fxj = Fj * cos(18°)
Fyj = Fj * sin(18°)

Diego's force (Fd) has a magnitude of 27 lbs and an angle of -15°:
Fxd = Fd * cos(-15°)
Fyd = Fd * sin(-15°)

Step 2: Calculate the x and y components of Corporal's force (Fc).
Since Corporal is holding the children at a standstill, the net force acting on Corporal will be equal in magnitude but opposite in direction to the combined forces of Juana and Diego.

Fxc = - (Fxj + Fxd)
Fyc = - (Fyj + Fyd)

Step 3: Calculate the magnitude of Corporal's force (|Fc|).
|Fc| = sqrt(Fxc^2 + Fyc^2)

So, once you determine the values of Fxj, Fyj, Fxd, and Fyd, you can calculate Fxc, Fyc, and |Fc|.