Given: F = 810 N, θ = 7º, G = 510 N, and φ = 112º. Find...
Given: F = 810 N, θ = 7º, G = 510 N, and φ = 112º.
Find the magnitude and the angle of the resultant vector.
The magnitude of the resultant vector is ___N.
The angle of the given vector is ___º.
Homework Answers
1a throught 1d please < G- (20 points total) A surface is parametrized as: x(φ, θ)-25in(n)...
1a
throught 1d please
< G- (20 points total) A surface is parametrized as: x(φ, θ)-25in(n) * Cos(0), y (φ, θ)- 25in(p) * Sin(θ), z-4Cos(p) for 0 φ π and 0 f 2m (a) Does this surface pass the point (1,2, 3)? If ye reason. (b) What is the normal vector of the surface at any given (p, 0) within the parameter domain? (e) What is the normal vector at ) (d) What is the equation for the tangent plane...
(f) (1 point) Using values v0 = 10 m/s, θ = 45◦ , φ = −12◦...
(f) (1 point) Using values v0 = 10 m/s, θ = 45◦ , φ = −12◦ ,
find r.
(g) (1 point (bonus)) For the case where φ = 0◦ (flat ground),
give the simplified expressions for horizontal displacement and
time of flight. Disregard the numerical values from previous
part.
2" (6 points) A projectile is launched with initial velocity vo at angle θ above horizontal The ground is sloped at angle φ w.rt. horizontal, where φ < θ 0
Determine the angles θ and φ so that the resultant force is directed along the positive...
Determine the angles θ and φ so that the resultant force is directed along the positive x axis and has a magnitude -20 N. J0 N 30 N
Suppose that F2 = 510 N. (Figure 1)
Suppose that F2 = 510 N. (Figure 1) Part A Determine the magnitude of the resultant forcePart B Determine the coordinate direction angle α of the resultant force. Part C Determine the coordinate direction angle β of the resultant force Part D Fi 400 N Determine the coordinate direction angle γ of the resultant force
Consider the following surface parametrization. x-5 cos(8) sin(φ), y-3 sin(θ) sin(p), z-cos(p) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for θ in [...
Consider the following surface parametrization. x-5 cos(8) sin(φ), y-3 sin(θ) sin(p), z-cos(p) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for θ in [0, 2T] and φ in [0, π] -3 cos(θ) sin(φ), 5 sin(θ) sin(φ),-15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 3 cos(9) sin(9),-5 sin(θ) sin(9), 15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 v 16 sin2(0) sin2@c 216 cos2@t9(3 cos(θ) sin(φ), 5 sin(θ) sin(φ) , 15 cos(q) 216 cos(φ)...
7. Let V = Pa(R), the vector space of polynomials over R of degree less than 2, with inner product Define φ E p by φ(g)-g(-1) a) By direct calculation, find f e V such that (S)-dg). You are given...
7. Let V = Pa(R), the vector space of polynomials over R of degree less than 2, with inner product Define φ E p by φ(g)-g(-1) a) By direct calculation, find f e V such that (S)-dg). You are given that A 1, V3-2v) is an orthonormal basis for V (you do not need to check this). b) Find the same f as in part a, using the formula for A(6) from class.
7. Let V = Pa(R), the vector...
Given a time-varying angle θ and a constant angle φ: Show that sin(θ(t) + (p) can...
Given a time-varying angle θ and a constant angle φ: Show that sin(θ(t) + (p) can be expressed as kisin(0(t)) + kcos(0 (t)) where kı and k are constants. (5 points) 5. where Kı
Let G be a finite group of order n. Let φ : G → G be the function given by φ(x) = z'n where rn E ...
Let G be a finite group of order n. Let φ : G → G be the function given by φ(x) = z'n where rn E N. If gcd(rn, n) = 1, show that φ s an injective map.
Let G be a finite group of order n. Let φ : G → G be the function given by φ(x) = z'n where rn E N. If gcd(rn, n) = 1, show that φ s an injective map.
(7) In this problem let X denote the vector space C(0, 1) with the sup norm. (a) Given f e X, define d(f) = f2. : X → X is differentiable, and Prove that φ find φ'(f). (b) Given f e X, define 9(f...
(7) In this problem let X denote the vector space C(0, 1) with the sup norm. (a) Given f e X, define d(f) = f2. : X → X is differentiable, and Prove that φ find φ'(f). (b) Given f e X, define 9(f) = J0 [f(t)]2dt. Prove that Ψ : X → R is differentiable. and find Ψ(f).
(7) In this problem let X denote the vector space C(0, 1) with the sup norm. (a) Given f e X,...
1a
throught 1d please
< G- (20 points total) A surface is parametrized as: x(φ, θ)-25in(n) * Cos(0), y (φ, θ)- 25in(p) * Sin(θ), z-4Cos(p) for 0 φ π and 0 f 2m (a) Does this surface pass the point (1,2, 3)? If ye reason. (b) What is the normal vector of the surface at any given (p, 0) within the parameter domain? (e) What is the normal vector at ) (d) What is the equation for the tangent plane...
(f) (1 point) Using values v0 = 10 m/s, θ = 45◦ , φ = −12◦ ,
find r.
(g) (1 point (bonus)) For the case where φ = 0◦ (flat ground),
give the simplified expressions for horizontal displacement and
time of flight. Disregard the numerical values from previous
part.
2" (6 points) A projectile is launched with initial velocity vo at angle θ above horizontal The ground is sloped at angle φ w.rt. horizontal, where φ < θ 0
Determine the angles θ and φ so that the resultant force is directed along the positive x axis and has a magnitude -20 N. J0 N 30 N
Consider the following surface parametrization. x-5 cos(8) sin(φ), y-3 sin(θ) sin(p), z-cos(p) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for θ in [0, 2T] and φ in [0, π] -3 cos(θ) sin(φ), 5 sin(θ) sin(φ),-15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 3 cos(9) sin(9),-5 sin(θ) sin(9), 15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 v 16 sin2(0) sin2@c 216 cos2@t9(3 cos(θ) sin(φ), 5 sin(θ) sin(φ) , 15 cos(q) 216 cos(φ)...
7. Let V = Pa(R), the vector space of polynomials over R of degree less than 2, with inner product Define φ E p by φ(g)-g(-1) a) By direct calculation, find f e V such that (S)-dg). You are given that A 1, V3-2v) is an orthonormal basis for V (you do not need to check this). b) Find the same f as in part a, using the formula for A(6) from class.
7. Let V = Pa(R), the vector...
Given a time-varying angle θ and a constant angle φ: Show that sin(θ(t) + (p) can be expressed as kisin(0(t)) + kcos(0 (t)) where kı and k are constants. (5 points) 5. where Kı
Let G be a finite group of order n. Let φ : G → G be the function given by φ(x) = z'n where rn E N. If gcd(rn, n) = 1, show that φ s an injective map.
Let G be a finite group of order n. Let φ : G → G be the function given by φ(x) = z'n where rn E N. If gcd(rn, n) = 1, show that φ s an injective map.
(7) In this problem let X denote the vector space C(0, 1) with the sup norm. (a) Given f e X, define d(f) = f2. : X → X is differentiable, and Prove that φ find φ'(f). (b) Given f e X, define 9(f) = J0 [f(t)]2dt. Prove that Ψ : X → R is differentiable. and find Ψ(f).
(7) In this problem let X denote the vector space C(0, 1) with the sup norm. (a) Given f e X,...
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