A river is flowing due east at 8 mi/h. A man heads his motorboat in thedirection N 30° E in the river. The speed of the motorboat relative to the water is 12 mi/h.(a) Express the true velocity of the motorboat as a vector.(b) Find the true speed and dfrection of the motorboat.

Q: A bullet is fired into the air with an initial velocity of 1,700 feet per second at an angle of 57°…

A:

Q: An airplane is on a heading of 235° at 600 km/h and a l10 km/h wind is blowing from due west.…

A:

Q: Find a unit vector in the direction of v. v = 12i - 35j

A:

Q: Express the vector in terms of it's length and direction. i + 2j - k

A: Solution:Given   i+2j+kTo express in terms of its length and direction.u=vvand v=vu

Q: A pedestrian walks at a rate of 6 km per hour east. The wind pushes him northwest at a rate of 13 km…

A:

Q: A balloon floats 18.5 kilometers east and then 24.6 kilometers north. What is the angle of the…

A:

Q: What is the magnitude of a vector = (-181- 12j)m/s?

A: Given,            v = (-18i + 12j) m/s

Q: Find the magnitude of the vector

A: The given vector is 0,7We know that in a vector a,b the magnitude is a2+b2

Q: what is the magnitude of the vector

A:

Q: Find the unit vector that has the same direction as the vector v = 6i.

A: For the vector ai∧+bj∧unit vector is given by ai∧+bj∧a2+b2

Q: forces acting at a point P are given as 30 pounds with N10°E and 80 pounds with N 80° E. Approximate…

A:

Q: Find the angle between the vectors, and

A:

Q: A dog searching for a bone walks 3.50 m south, then runs8.20 m at an angle 30.0° north of east, and…

A: According to the given function draw the graph of the function:

Q: Calculate the force (in Newtons) required to push a 50kg wagon up a 0.2 radian inclined plane. One…

A: Solution:

Q: Sketch the vector v = -3i - 4j as a position vector and find its magnitude.

A: Given: v = -3i - 4j

Q: Find the vertical component of a vector, where the inclination  Θ of the vector from the horizontal…

A:

Q: A bullet is fired into the air with an initial velocity of 950 feet per second at an angle of 67o67o…

A: Given: A bullet is fired into the air with an initial velocity of 950 feet per second at an angle of…

Q: Find the unit vector in the same direction as v = 4i - 3j. Then verify that the vector has magnitude…

A: Consider the following vector: v→=4i^-3j^ Consider the following formula: unit…

Q: Find the unit vector that has the same direction as the vector v = 4i - 2j.

A: the given vector is v=4i-2j

Q: Find the unit vector that has the same direction as the vector v. 31

A:

Q: Find a unit vector in the direction of the given vector

A: Given:        v=-9,-12 Unit vector formula is the vector divided by its magnitude.  The formula for…

Q: Find the unit vector in the same direction as v = 2i - 3j -6k

A: Given vector is v=2i-3j-6k. To find the unit vector in the same direction of the given vector.…

Q: Determine the angle that the vector [-1, -1] makes with the positive horizontal X-axis

A:

Q: A motorboat sets out at 10 am from a position (-6i – 2j) km relative to a marker buoy, and travels…

A: please see the next step for solution

Q: Find the unit vector that has the same direction as the vector v = 3i - 2j.

A: Given vector is v→=3i-2j We have to find unit vector that has same direction as given vector.…

Q: Find the magnitude of the vector.

A: The given question is taken from the vector in which we have to find the magnitude of the given…

Q: What is the unit vector with the same direction as the vector v = 2i - 7j? Write as a linear…

A:

Q: Find the angle between the vectors and .

A: Given vectors a=-2i-j+3k b=2i+j-3k

Q: A small plane is flying horizontally due east in calm air at 150 mi/hr when it is hit by a…

A: Let's find.

Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction

A:

Q: Find the direction angle 0 of the vector v = .

A:

Q: A vector is described as "A plane with an airspeed of 450 miles per hour is flying in the direction…

A:

Q: A river flows due south at 3 mi/h. A swimmer attempting to cross the river heads due east swimming…

A: It is given that, a river flows due south at 3 mi/h. A swimmer attempting to cross the river heads…

Q: Find the unit vector in the direction of

A: Unit vector in the direction <-2, -5> Unit vector have magnitude 1

Q: A leaf is floating on a river to the S30°E at 6 km/h. A wind blows to the west at a rate of 3 km/h.…

A: Given : Leaf is floating at 6 km/h and wind is blowing at 3 km/h

Q: A volleyball is hit when it is 4 ft above the groundand 12 ft from a 6-ft-high net. It leaves the…

A: Given information: A volleyball is hit when it is 4 ft above the ground and 12 ft from a 6-ft-high…

Q: find the component form of the vector. The vector 2 units long in the direction 4i - j

A: Given vector is u = 4i – j. So, the unit vector in the direction of the given vector is

Q: Express the vectors in terms of their lengths anddirections. √2i + √2j

A: If a vector is defined as: v→=ai+bj Then, the length or magnitude of the vector is: |v→|=a2+b2 The…

Q: Find the unit vector in the direction opposite (-2, –1). to y =

A:

Q: A pedestrian walks at a rate of 6 km per hour east. The wind pushes him northwest at a rate of 13 km…

A: We can find the answer as below

Q: A plane is flying with an airspeed of 140 miles per hour and heading of 155∘degrees. The wind…

A: Let P be the speed of the plane. Let W be the direction of the wind. Let T be the ground speed and…

Q: Find the magnitude of the vector u =

A:

Q: Find the unit vector in the same direction as

A:

Q: A sailboat is sailing at a speed of 6 knots at a true bearing of 220°. Give the velocity of the…

A: First represent the vector on coordinate plan than break the components along x & y-axis.

Q: Find a unit vector in the direction of the vector v = .

A: Given a vector v=<-2,2>. We need to find a unit vector in the direction of 'v'. Let's begin.

Q: A bullet is fired into the air with an initial velocity of 1,900 feet per second at an angle of 80°…

A: Consider the diagram below for the velocity vector.

Q: The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the…

A: The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the…

Q: find the component form of the vector. The vector obtained by rotating <0, 1> through an angle…

A: Find the component form of the vector. The vector obtained by rotating <0, 1> through an angle…

Q: A bullet is fired into the air with an initial velocity of 897 feet per second at an angle of 53°…

A:

Q: Find the unit vector in the same direction as v = 5i - 12j. Then verify that thevector has magnitude…

A: Unit vector in same direction vectorvector's magnitude