An airplane propels itself eastward with speed v. A crosswind with speed u is directed at...

An airplane propels itself eastward with speed v. A crosswind with speed u is directed at an angle θ (0 < θ < π) north of east. What is the distance travelled by the plane after a time t?

Expert Solution

Let positive x be along east and positive y be along north.

Then,velocity of airplane relative to air = v

Velocity of wind = u cos + u sin

So, net velocity of the airplane = velocity of airplane relative to air+velocity of wind

= (v+ucos)+(usin)

Magnitude of velocity = [(v+ucos)^2+(usin)^2]^0.5

= [v^2+(ucos)^2+2uvcos+(usin)^2]^0.5

= [u^2+v^2+2uvcos]^0.5

So, distance= (magnitude of velocity)*time = [(u^2+v^2+2uvcos)^0.5]*t

genius_generous answered 2 years ago

Let u be the magnitude 5 directed towards the north of v of magnitude 3 directed...

Let u be the magnitude 5 directed towards the north of v of magnitude 3 directed 20°W of N. Specify the vectors: uv, vu, uu, u(v + u), and -2u(7v).

A rooster escapes from the farm. The rooster propels itself off the roof of a 160...

A rooster escapes from the farm. The rooster propels itself off the roof of a 160 foot tall barn at an angle of 40° and has an initial velocity of 15 m/s. After traveling for 30 seconds at a constant speed, the rooster decides to lower down by completely stopping all flying motion. After free falling 10 meters, an eagle traveling directly leftward hits the rooster. The eagle was flying at a constant 45 m / s. a) Draw a...

If V = U ⊕ U⟂ and V = W ⊕ W⟂, and if S1: U...

If V = U ⊕ U⟂ and V = W ⊕ W⟂, and if S1: U → W and S2: U⟂ → W⟂ are isometries, then the linear operator defined for u1 ∈ U and u2 ∈ U⟂ by the formula S(u1 + u2) = S1u1 + S2u2 is a well-defined linear isometry. Prove this.

A speed field; It is defined by V(u,v)=(V1/L)(-xi+yj) , here V1 and L are fixed. This...

A speed field; It is defined by V(u,v)=(V1/L)(-xi+yj) , here V1 and L are fixed. This flow is 2 dimensional and stable. (a)In which position in the flow area does the velocity equal the velocity V1? Make an outline of the speed field by drawing arrows for x>=0 , these arrows should represent fluid velocity in representative positions. (b)Draw the flow line. (dx/u=dy/v)

Prove that if U, V and W are vector spaces such that U and V are...

Prove that if U, V and W are vector spaces such that U and V are isomorphic and V and W are isomorphic, then U and W are isomorphic.

show that for any two vectors u and v in an inner product space ||u+v||^2+||u-v||^2=2(||u||^2+||v||^2) give...

show that for any two vectors u and v in an inner product space ||u+v||^2+||u-v||^2=2(||u||^2+||v||^2) give a geometric interpretation of this result fot he vector space R^2

A DAG is a directed graph that contains no directed cycles. Define G = (V, E)...

A DAG is a directed graph that contains no directed cycles. Define G = (V, E) in which V is the set of all nodes as {v1, v2, ..., vi , ...vn} and E is the set of edges E = {ei,j = (vi , vj ) | vi , vj ∈ V} . A topological order of a directed graph G = (V, E) is an ordering of its nodes as {v1, v2, ..., vi , ...vn} so that...

A 200 kg sled that is 40m long is sliding eastward at a speed of 5...

A 200 kg sled that is 40m long is sliding eastward at a speed of 5 m/s relative to the icy ground below. A 60 kg human is standing at the eastern edge of the sled and suddenly begins running westward at a constant speed of 10 m/s relative to the center of mass of the system that consists of the sled and the human. 1) Explain why the sled speed increase after the human starts to run. 2) Determine...

Let U be a subspace of V . Prove that dim U ⊥ = dim V...

Let U be a subspace of V . Prove that dim U ⊥ = dim V −dim U.

Suppose u, and v are vectors in R m, such that ∥u∥ = 1, ∥v∥ =...

Suppose u, and v are vectors in R m, such that ∥u∥ = 1, ∥v∥ = 4, ∥u + v∥ = 5. Find the inner product 〈u, v〉. Suppose {a1, · · · ak} are orthonormal vectors in R m. Show that {a1, · · · ak} is a linearly independent set.

Question