Vector + right triangle - practice problems
Number of problems found: 51
- Triangle 82
Triangle PQR has vertices located at (2, 2), (5, -4), and (-4, -1). What type of triangle is triangle PQR? - Horizontal 83148
The bend has a radius of r = 100 m and is inclined at an angle of 20° to the horizontal plane (= tilt angle). What is the safe (the "best") speed to go through this curve? Sketch the picture regarding NIVS, mark the forces, and calculate. - Meridian ground speed
The plane flies south at an average speed of 190 km/h, and the wind blows from west to east at a speed of 20 m/s. How fast and in what direction (relative to the meridian) will the plane move relative to the ground? - Crosswind
A plane is traveling 45 degrees N of E at 320 km/h when it comes across a current from S of E at 115 degrees of 20 km/h. What are the airplane's new course and speed?
- North + west
Find the magnitude of the resultant of the given vectors: vector 1:2 m/s, north vector 2:7 m/s, west - Calculate 66814
Calculate the area and perimeter of the right triangle ABC if A [5.5; -2.5] B [-3; 5] C [-3; -2.5] - Northeast 66694
Katka and Honza rode out on their scooters at the same time. Katka drove at a speed of 4.5 km/30 min, and Honza drove at a speed of 4 km/20 min. a) how many m did they travel in 2 minutes if they went in the opposite direction? b) how many miles did they - Perpendicular 62844
A body with a mass of 4 kg hits an obstacle at a speed of 10 m/s. After the collision, the body continued to move at a speed of 6 m/s, while the direction of this speed was perpendicular to the direction of the speed before the collision. Find: a) change - Raindrops
The car runs on a horizontal track at a constant speed of 20 m2-1. It is raining. Raindrops fall in a vertical direction at a speed of 6 m/s. a) How fast is the speed of the drops relative to the car windows? b) What is the angle of the raindro
- Three
Three points are given: A (-3, 1), B (2, -4), C (3, 3) a) Find the perimeter of triangle ABC. b) Decide what type of triangle the triangle ABC is. c) Find the length of the inscribed circle - Coordinates 59863
The endpoint of the vector is given, which is located at the origin of the Cartesian system Oxy. Determine the coordinates of the vector and its magnitude, and sketch it: P[3,4]; Q[-2,7]; S[-5,-2] . .. i.e., Vectors PO, QO, SO - Lengths of medians from coordinates
There is a triangle ABC: A [-6.6; 1.2], B [3.4; -5.6], C [2.8; 4.2]. Calculate the lengths of its medians. - Angle ASB
On a circle with a radius of 10 cm and with a center S, the points A, B, and C are given so that the central angle ASB is 60 degrees and the central angle ASC is 90 degrees. Find the length of the circular arc and the amount of AB and AC offsets. - Isosceles 48443
Three equal positive charges Q are located at the vertices of an isosceles right triangle ABC. The right angle is at vertex A. The length of side AB is 1m. What is the electric field strength at the center S of side BC, i.e., what force would act on a pos
- The bomber
An aircraft flying at an altitude of 1260 m. From what distance in front of the target must a parachute load be dropped from an airplane? The load slopes at a speed of 5.6 m/s and moves in the direction of movement at 12 m/s. What is the direct distance o - Space vectors 3D
The vectors u = (1; 3; -4), v = (0; 1; 1) are given. Find the size of these vectors, calculate the angle of the vectors, and the distance between the vectors. - Mass point
Two equal forces of 30 Newtons act on a mass point. Find the magnitude of the resultant force if these forces form an angle of 42°. - Two-dimensional 36453
Two of its inhabitants stand at one point in the land of two-dimensional beings. Suddenly, they both start running at the same moment. Resident A runs north at 5m/s, and resident B runs east at 12m/s. Calculate how fast they are moving away from each othe - Vectors abs sum diff
The vectors a = (4,2), b = (- 2,1) are given. Calculate: a) |a+b|, b) |a|+|b|, c) |a-b|, d) |a|-|b|.
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