The two hot-air balloons in the drawing are 48.2 m and 61.0 m above the ground. A person in the left balloon observes that the right balloon is 13.3° above the horizontal. What is the horizontal distance x between the two balloons?

Q: A vector A has the following components, Ax = 5.1 cm; Ay = 2.9 cm. What is the magnitude of this %3D…

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Q: Vector A has magnitude of 8 m and vector B has magnitude of 7.8 m. If the angle between the two…

A: Given data, Magnitude of vector A = 8 m Magnitude of vector B = 7.8 m Angle between vector A and B =…

Q: What is the angle between vector Å = 5i + 2j + 9k with z-axis? 80° 45.80 30.9° 61.5°

A: angel between A→ = 5i^ + 2j^ + 9K^ and z - axis. The formula to find the angle between vector and…

Q: Given the following four force vectors in terms of their magnitude and directions, find the…

A: Given,  Four vectors in terms of their magnitude and direction. F1 = 534.7 N @ 135.4°F2 = 987.6 N @…

Q: The components of vector A are: Ax=5.6 Ay= -4.7 What is the angle between vector A and positive…

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Q: Vector A has a magnitude of 2.00 m and vector B has a magnitude of 5.00 m. If the direction of each…

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Q: Write the final magnitude and direction of the resultant vector. Include a properly labeled diagram…

A: solution as

Q: Vectors A→A→ and B→B→ both have a magnitude of 8. If their resultant has a magnitude of 10, what is…

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Q: The vector in the drawing has a magnitude of 712 units. Determine the (a)x and (b)y components of…

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Q: Vector V with magnitude | V | forms an angle with the positive x-axis. Give the magnitude of the…

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Q: For the vectors á (3.0 m )î + (4.0 m )j and B = (5.0 m )i + ( – 2.0 m 3, give d + b in (a) unit-…

A: a) a+b = (3i+4j)+(5i-2j) a+b= 8i-2j Magnitude of (a+b) = √(8²+2²) = √68 So unit vector =…

Q: The y component of a vector K of magnitude k= 8cm shown in the figure below is K, = +5 cm. What is…

A: The projection of this vector on x axis is given by: k cosθ The projection on the y axis : k sinθ =5…

Q: Two displacement vectors when added produce a resultant vector of magnitude 50.0 km pointing 60.0°…

A: We will first break the vectors into the component in the perpendicular axes. We split them in the X…

Q: Vector A is 9 m, 60.0o North of East and Vector B is 3 m 30.0o West of North. What is the resultant…

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Q: Vector A has a magnitude of 8 units and makes an angle of 45.0 degrees with the positive x-axis.…

A: A→ = 8 ×(cos45oi^ + Sin45oj^) A→ = 5.65i^ + 5.65j^B→ = -8i^

Q: Find the x− and y− components of the vectors A~, B~ , C~ , and D~ . Take A = 10.0, B = 7.00, C =…

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Q: We have two vectors A=(57.8, 12.5 degrees) and B=(19.0, 140.3 degrees). What is the x-component of…

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Q: A position vector that belongs to the xy plane is described by the components (x, y) - (-3.00 m,…

A: Cartesian coordinates(X,Y) in polar coordinates are given by X=rcos(theta) Y=r sin(theta) Where r is…

Q: Vector A= 1.008 -2.00P, vector B =3.008 + 4.009. what is the direction of vector 56.3…

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Q: vector A are: Ax = 5.1 m and Ay= -5 m and the components of B are: Bx= -2.6 m and Ay = -4.3 m. What…

A: This question is based on resultant of vectors.

Q: Two displacement vectors when added produce a resultant vector of magnitude 50.0 km pointing 60.00…

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Q: Vector A has a magnitude of 8.0 m, South and vector D has a magnitude of 10.0 m, 53° W of N. Find…

A: Given: The magnitude of vector A  is 8 m in the south direction. The magnitude of vector D is 10 m…

Q: B (15.0 m) D (10.0 m) 30.0 53.0 25.00 Č (12.0 m) A (8.00 m) ne X component of the vector D shown in…

A: 1.  Suppose given that Vector is R and it makes angle  with +x-axis, then it's components are given…

Q: 4 A -2 4 -2 Consider the two vectors, A and B, in the figure. The x and y components of both vectors…

A: Addition of two vectors A→=axi^+ayj^+azk^ and B→=bxi^+byj^+bzk^ is given by-…

Q: QUESTION 1 A= 2.27 î+ 5.41 + 9.45 j + = ? Input answer using 3 significant figures 11.1 QUESTION 2…

A: 3 significant figures means in answer there should be 3 digits after decimal point.  Correct Answers…

Q: Given that vectors T = + 2.00x + 6.00y – 4.00z and D = 2.00x – 3.00y – 4.00z The angle between the…

A: Given that Vector T = +2x + 6y - 4z Vector D = 2x - 3y - 4z

Q: Question 1/13 The angle (in degree) between vector A= 10i+3j-4k and vector B= i-5j+6k is 1. O 150.8…

A: Given data: The vector A is A=10i+3j-4k. The vector B is B=i-5j+6k.

Q: Vector A has a magnitude of 8 units and makes an angle of 45.0 degrees with the positive x-axis.…

A: Given : A→ = 42 i^ + 42 j^            B→ = - 8 i^

Q: A vector ?⃗ = (−1.2 m)?̂+ (1.8 m)?̂. Find the magnitude and angle (between 0° and 360°, measured…

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Q: Consider the following two vectors:U = 1.3i + 2.2j + 4.1k V = -5.5i - 6.5j + 11.3k What is the…

A: Given: U = 1.3i + 2.2j + 4.1k   V = -5.5i - 6.5j + 11.3k

Q: A ball is projected with velocity 10 m/sec at angle of 30° with the horizontal surface. The angle…

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Q: What is the component of the force vector G = (3.0i + 4.0j  + 10.0k  )N along the force vector H =…

A: Given: G→=3.0i^+4.0j^+10.0k^ N H→=1.0i^+4.0j^ N

Q: Two vectors are given by d = (5.0 m)i - (6.0 m)ĵ + (1.0 m)k %3D and b = (-1.0 m)î + (1.0 m) ĵ + (2.5…

A: Given,a→ = 5.0 m i^ - 6.0 m j^ + 1.0 m k^b→ = -1.0 m i^ + 1.0 m j^ + 2.5 m k^

Q: For the vectors V1 = 10 units and V2 = 7.5 %3D units shown in the figure, V1 45° 30 V2

A: V1= 10 units  V2= 7.5 units

Q: Find the angle between the vectors A = and B = . (a) 50.0 (b) 178 (c) 120 (d) 98.0

A: Vector A  = -4i -2j Vector B = 3i + 1j

Q: Vector a has a magnitude of 12 units and makes a 60° angle with the +x axis. What is the y component…

A: The y component of vector α is    αy=αsinθ Here α=12 units and θ=60o

Q: The three vectors in the figure have magnitudes a= 3.20 m, b 2.70 m, and c 10.3 m and angle 0=…

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Q: Given four vectors: 25 newtons 50 degrees north of east; 16 newtons 75 degrees south of east; 10…

A: Given: A=25 N (50 N of E)B=16N (75 S of E)C=10 N (35 E of N)D=30N (S)

Q: Find the resultant vectors. 1. A 10 M, NORTH = B = 20 M, NORTH 2. C= 15 M, WEST D = 20 M, WEST 3.…

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Q: Determine the angle between the directions of vector A = 3.00i + 1.00j and vector B = -3.00i + 3.…

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Q: What are the components of the following Vector?  D = 30.0 km @ 70.0 degrees below +x-axis

A: Given: The vector has magnitude D = 30 km. Angle with +x axis = 70 degree clockwise direction.

Q: Two vectors A and B have precisely equal magnitudes. For the magnitude of Á + B to be 100 times…

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Q: In a computer game, an airplane starts at the (x,y) coordinate (1,5) in cm on the curve…

A: Consider the given equation. On differentiating the above equation with respect to t, we have, At…

Q: 4. A vector A has component Ax = 12 m and Ay =5 m. What is the angle that vector A makes with the Y…

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Q: Vector A has a magnitude of 8 units and makes an angle of 45.0 degrees with the positive x-axis.…

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Q: Two vectors are given by A = 4.00 i + 7.00 j and B = 5.00 i - 3.00 j. What is %3D the resultant…

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Q: (8c3p28) Given two vectors a = 3.5i -3.8j and b =6.8i+8.4j what is the magnitude (in m) of the…

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Q: For the vectors and shown, find the magnitude and direction of (a) the vector sum + (b) the vector…

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Q: 4. Vectors A and B have magnitudes of 3 units and 4 units, respectively. What is the angle between…

A: The dot product of two vectors is:

Q: Consider the following 2 vectors: A –3.29 ; +5.49; B =1.64 ;+4.09; What is A. B? Please express your…

A: Given data:  A→ = 3.29i^ + 5.49j^B→ = 1.64i^ + 4.09j^ Required: The dot product of vector A and…