The support ropes, each with a tensile strength of 433 N, support a load hanging in an O-ring.

The angle α between the ropes and the horizontal ceiling is 10°.

How large a load can the ropes support when no safety factors are used? Give your answer to an accuracy of 1 N.

The boat's speed in calm and non-flowing water is 15 knots. In water flowing from west to east (draw from left to right ), the boat is directed straight south (draw downwards), and then the boat moves in a direction that is 13° southeast (draw to the right).

What is the water's flow speed? Give your answer to two decimal places of a knot.

The endpoint of vector = [3, -2, 1] is (3, 4, 4).

How far is the origin point of from the origin?

Give your answer to one decimal place.

What is the length of the vector drawn from the point (6,7,8) to the point (8,1,2) ?

Give your answer to one decimal place.

At point P, there is a ring attached to three ropes. The ropes are pulled horizontally with forces as shown in the diagram below, with magnitudes

In which direction does the ring start to move? Give the angle relative to the vector with an accuracy of one degree.

The diagram only reveals the numerical angles of the forces' directions. The vectors' lengths and directions do not reflect reality; use the given numerical values instead.

In the tetrahedron shown in the image, points P and Q are on segments BD and DC such that the ratios BP:PD = 2:3 and DQ:QC = 1:4. Express the vector using vectors , , and .

Choose the correct option letter from the options listed below.

A)  

F) none of the options mentioned above.

Two tugboats are pulling a raft in different directions and as shown in the diagram.

The raft moves in the direction . By what percentage is larger than ?

Give your answer with an accuracy to one percent.

(The diagram only shows the directions of the forces, not their magnitudes.)

How long is the vector in a three-dimensional rectangular coordinate system?

Give your answer to one decimal place.

h3 03

The wall is fitted with a support structure made of two beams as shown in the accompanying image, from whose corner hangs a 1200 N load 𝐹⃗.

How much force is trying to stretch the upper beam?

Give your answer in Newtons to an accuracy of one Newton.

The support forces in beams in such situations are always aligned with the beam; either tensile or compressive.

The situation is static, meaning there is no movement, so the total sum of all forces is .

A structure consisting of two support beams is attached to the wall as shown in the adjacent image, with the upper beam forming a 33° angle with the vertical wall. A 1000 N load hangs from the corner of the beam structure.

How many Newtons of compression force are exerted on the lower support beam?

Give your answer with an accuracy of one Newton.

The support forces in beams in such situations are always aligned with the beam; either tensile or compressive.

The situation is static, meaning there is no movement, so the total sum of all forces is .