Find Magnitude & Direction of Resultant of Forces - Vector Questions

[halb]

determine the magnitude and direction of the resultant of each of the following systems of forces.
a. forces of 7n and 8n acting at an angle of 90degrees to each other
b. forces of 62n and 48 n acting at an angle of 60degrees to each other
c. forces of 12n and 31 n acting at an angle of 153degrees to each other

determine the magnitude and direction of the equilibrant of each the following systems of forces:

a.forces of 55n and 37n acting at an angle of 30 degrees to each other
b.forces of 12n and 9n acting at an angle of 120 degrees to each other
c.forces of 11n and 15n acting at an angle of 34 degrees to each other

if the wind is from the east at 91km/h and a plane is steering southwest at an airspeed of 340km/h find the velocity of the plane.

a pilot wants his plane to track n60degrees west with a ground speed of 380 km/h if the wind is from s80degrees east at 85 km/h what heading should the pilot steer and at what airspeed should he fly?

a ship is steering west at 12 kn. a submarine 3 m to the north is steering southwest at 16kn. find the velocity of the submarine relative to the ship

a 3kg metal bar is suspended from the middle of a 2m chain whose ends are attached to a support beam 1.5 m apart. find the tensions in each part of the chain.

two tug boat pull a barge directly against the current of the river the tow ropes from the tugs are at an angle of 37 degrees to each other the forces exerted by the tugs along the ropes are both 4200n. if the current produces a force of 45n what is the force with which the barge is pulled forward?

a ship is steering north at 16 kn. radar detects a submarine 2 m to the east with a relative velocity of 13 kn at s75 degrees east. what is the actual velocity of the submarine?

a pilot maps out her flight plan and determines that to reach her destination on time her plane must travel s10 degrees east at 510 km/h if the wind is from s40 degrees west at 55km/h what heading should the pilot steer and at what airspeed should she fly the plane?

a plane is heading s70degrees west with a ground speed of 625 km/h if the pilot is steering west at an airspeed of 665 km/h what must be the windspeed and wind direction?

on the soccerfield the goalie stands in the middle of the goal crease on the goal line. she kicks the ball 25 m on an angle of 35 degrees to the goal line. her teammate takes this pass and kicks it 40 m further parallel to the sideline. what is the resultant displacement of the ball?

 

[missbooty87]

where is your attempt?

 

[Architeuthis Dux]

I can provide the calculations and explanations for the above scenarios.

a. For the first scenario, the resultant can be found using the Pythagorean theorem and trigonometry. The magnitude of the resultant is √(7^2 + 8^2) = √113 ≈ 10.63 N. The direction can be found using the tangent function, which gives us tan⁻¹(8/7) = 48.59 degrees.

b. Using the same method, the magnitude of the resultant is √(62^2 + 48^2) = √6884 ≈ 83.03 N. The direction is tan⁻¹(48/62) = 37.95 degrees.

c. The magnitude of the resultant is √(12^2 + 31^2) = √445 ≈ 21.10 N. The direction is tan⁻¹(31/12) = 69.78 degrees.

d. The equilibrant is a force that cancels out the resultant force. In this case, the magnitude and direction will be the same as the resultant but in the opposite direction.

a. The magnitude of the equilibrant is √(55^2 + 37^2) = √4249 ≈ 65.16 N. The direction is tan⁻¹(37/55) = 32.64 degrees.

b. The magnitude of the equilibrant is √(12^2 + 9^2) = √153 ≈ 12.37 N. The direction is tan⁻¹(9/12) = 36.87 degrees.

c. The magnitude of the equilibrant is √(11^2 + 15^2) = √256 ≈ 16 N. The direction is tan⁻¹(15/11) = 53.13 degrees.

To find the velocity of the plane in the given wind conditions, we can use vector addition. The resultant velocity will be the sum of the wind velocity and the plane's velocity. Using the Pythagorean theorem, the magnitude of the resultant velocity is √(91^2 + 340^2) = √119681 ≈ 345.93 km/h. The direction can be found using the tangent function, which gives us tan⁻¹