Angle + vector - math problems

Number of problems found: 25

  • Bearing - navigation
    A ship travels 84 km on a bearing of 17° and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
  • Angled cyclist turn
    The cyclist passes through a curve with a radius of 20 m at 25 km/h. How much angle does it have to bend from the vertical inward to the turn?
  • Angle ASB
    On a circle with a radius of 10 cm and with a center S, the points A, B, 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 circle arc and the amount of AB and AC offsets.
  • Two forces
    Two forces with magnitudes of 25 and 30 pounds act on an object at 10° and 100° angles. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and your final answer.
  • Airplane navigation
    An airplane leaves an airport and flies to west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
  • Scalar dot product
    Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120°
  • Forces
    Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?
  • Dodecagon
    Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
  • 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°.
  • Ballistic curve
    The soldier fired the ballistic grenade at a 45° angle. The first half ascended, the second fall. How far and height it reached if his average speed was 1200 km/h, and 12 seconds took from the shot to impact.
  • 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, the distance between the vectors.
  • Decide 2
    Decide whether points A[-2, -5], B[4, 3] and C[16, -1] lie on the same line
  • Two people
    Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph on the other road. How long will it take for them to be 20√5 km apa
  • Bearing
    A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
  • Resultant force
    Calculate mathematically and graphically the resultant of three forces with a common center if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
  • Two forces
    The two forces F1 = 580N and F2 = 630N, have an angle of 59 degrees. Calculate their resultant force, F.
  • Triangle
    Plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3] give Triangle KLM. Calculate its area and its interior angles.
  • Vector sum
    The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
  • Three vectors
    The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point to balance. Determine the angles of each two forces.
  • Find the 10
    Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular, parallel, what angle does each of the lines make with the x-axis, find the angle between the lines?

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