Answered: (5) A particle moves in space, its…

(5) A particle moves in space, its position is specified by the position vector r(1) = (1,r,t sint), t20. Then find at t=7 sec onds (a) Its position; (b) Its velocity (c) its acceleration

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

See similar textbooks

Related questions

Q: 1. Find the second derivative of the parametric equations_x = a cost and y = b sin t

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

Q: In what direction from the point (1,-1) is the instantaneous rate of change of f(x.y) = 8x* – 10x?y?…

Q: .3 At which point P does the curve r(t) = ( 2t have the tangent vector (24, -8, 3) ? (a) P(2, 2, 2)…

A: Here we have, the given curve is r→(t)=2t3, 2t2, 3t-1 now differentiate with respect…

Q: Find the parametric equations of the tangent line to the curve represented by the vector function…

Q: 9. An object moving along a curve in the xy-plane has position (x(t),y(t)) at dy dx :=1+ tan(r²) and…

A: According to Bartleby q&a guidelines I will attempt only one question

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: A particle at (1,0,0) starts moving in space in such a way that its position vector at any time t> 0…

A: Here, the position vector is given as R→(t)=cos t+ t sin ti^+sin t- t cos tj^+t2 k^. (a) The tangent…

Q: Express the velocity and the acceleration of a moving point p(r,0)

A: We have given a curve in polar coordinate : r=1+sin(θ) with θ=t2…

Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (sin(3t), cos(t), cos(: OS…

Q: Example 4 Find the directional derivative off(x. y. z) = xy -v+at the point (1,-2,0) in the…

A: If f is differentiable at x,y,z , then f has a directional derivative in the direction of any…

Q: Suppose r(t) = cos(nt) i + sin(t) j+ 3tk represents the position of a particle on a helix, where z…

A: Given the vector

Q: 5. Find the parametric equations of the line tangent to the curve C defined by the vector equation…

A: To find the parametric equation of the given tangent to the curve. The vector equation of the curve…

Q: Find the tangential and normal components of the acceleration vector for the curve 7(t) = (- 3t,…

Q: A particle moves in space along a path whose parametric equations are given by x1 = b sin(wt), x2 =…

Q: 2. If a particle's position is given by r(t) = <t ₁2 cost, sint), find the IN velocity,…

A: Given: particle position, r→t=t, 2 cos t, sin t We have to find the velocity, acceleration and speed…

Q: 3. A unit vector tangent to the curve y x2 at the point (2, 4).

A: We are entitled to solve only one question at a time so we will answer only the first question.…

Q: Q2. A point is moving along a curve whose position vector is Find : the acceleration components at /…

A: Consider the given position vector

Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t))i + (5 sin(6t)) j +…

Q: A force with magnitude 35 N acts directly upward from the xy-plane on an object with mass 7 kg. The…

Q: A point, p, is moving with acceleration 6t j - k at time t. If at t 1, the coordinates of P are (1,…

A: Answer

Q: x-1 y-2 z-1 2 -6 7 1 F(t) = ( 21 + ¹ )i + ¹/ (m² − 3)} j + t√21³-1k at t=1 1 4 (c) show that the…

Q: if the velocity function vector v = 3t 1+ tJ- 2k find the acceleration( a). -

Q: 4. Determine the directional derivatives of $(x, y) = tan"2+3 sin ). at the point (1,1) in the…

Q: an object is moving in 3-dimensional space with velocity vector v(t)=(sin(t),t,t^2) starting at…

A: Consider the given velocity vector: vt=sint,t,t2 Find the position vector: Integrate velocity vector…

Q: 25. A particle is located at (1, 1,0) at time t = 0 and it follows a path whose velocity vector is…

A: Let's find.

Q: 6. A particle at (1,0,0) starts moving in space in such a way that its position vector at any time t…

A: The vector equation of the tangent line of the parametric curve r→t at point P is expressed by…

Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t)) i + (5 sin(6t)) j+…

A: Given the vector function, r(t), we call r′(t) the tangent vector provided it exists and provided…

Q: 2. An object moving along a curve in the xy-plane has position (x(t),y(1)) at time t with the…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: b. Find the directional derivative of the function z = x3 – y3 at the point M(1,1), in the direction…

Q: 1. (a) Find the rate of change of the function f(x,y) = x² + 3ry at the point (3,2) in the direction…

A: Given fx,y=x2+3xy point 3,2 vector v=3i+4j

Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (cos(t), sin(3t), cos(3t))…

Q: The parametric equations of a curve are given by x = In (VE +1) and Vt + y = cosh-(2t). X = dy when…

Q: x-1_y-2_z-1 -6 (c) show that the line 2 7 curve F(t) = (21+²) 1+ ²+ (in ²²-3) 1+1√21³²-1k at 1=1 i+…

Q: A particle moving along a curve in the xy-plane has position (x(1),y(t)) at time dy dx t with dt =…

Q: The circular plate rotates around its axis at constant angular velocity. The particle on the plane…

Q: 3. A particle moving along a curve in the xy-plane has position (x(t1),y(t)), with x(1)= 2t +3sin t…

A: Velocity is equal to the first derivative of position vector Let x =f1t and y =f2t then velocity…

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

Q: Find the directional derivative of the function f = In (x² + y2) at the point P(4,5) in the…

A: By Bartleby policy I have to solve only first one as Q)3)a) and Q)3)b) are unrelated problems.These…

Q: Find the parametric equations of the tangent line to the curve represented by the vector function 7…

A: Topic = Vector

Q: Find a unit vector that is normal to the level curve of the function f(x, y) = 5x + 6y at the point…

Q: A particle moves along the graph of y = cos r so that the r-component of acceleration is always 2.…

A: Use the given information carefully.

Q: 2. The position vector of the particle is 1 R = î cos(t) + 3 sin(t) + k log (0 <t < n/2). sin t' (a)…

Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (sin(3t), cos(t), cos(3t))…

Q: Example 4. Find the tangent vector at the point (2,4). on the top half of the circle x² + y² = 1…

A: Introduction: For a given vector curve rt, the equation that represents the tangent line to the…

Q: 5) A ball is bounced directly south, with an initial velocity of 10 m/s off the ground, with an…

A: Consider the provided question, sketch a diagram according to the given question,

Q: Choose the direction vector for which the function f defined by f(x, y)= sin(5x) cos(3y) has the…

Q: A particle moving along a curve in the xy-plane has position (x(t), y(t)) = (-9 sin(9t), 3t² + 10t),…

A: Solved below

Q: The velocity of a particle moving in the xy plane is given by the parametric equations dx/dt=…

A: The given parametric equations of the particle is dxdt=-2t sin2t and dydt=2t cos2t. Evaluate the…

Q: A particle at (1, 0, 0) starts moving in space in such a way that its position vector at any time t…

Question

100%

(5) A particle moves in space, its position is specified by the position vector
r(t) = (1,t,t sint), t20. Then find at t=7 sec onds
(a) Its position;
(b) Its velocity
(c) its acceleration
(d) The equation of the tangent line to the trajectory;

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Component Form$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

A particle is moving with velocity V(t) = ( pi cos (pi t), 3t2+ 1) m/s for 0 ≤ t ≤ 10 seconds. Given that the position of the particle at time t = 2s is r(2) = (3, -2), the position vector of the particle at t is?
The equation for the position vector r(t) of the particle at time t is
at an air show, a jets trajectory is following the curve y=x^2 if when the jet is at point (1,1), it has a speed of 500 km-h, determine its tangent vector to this point. Ans: r'=(100x5^1/2, 200x5^1/2
Calculate the velocity and acceleration vectors and the speed at the time indicated.r(θ) =〈sin θ, cos θ, cos 3θ〉, θ = π/3
What is the velocity vector of the particle at time t=2?
find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 + sin t) and θ = 1 - e-t
give the position vectors of particles moving alongvarious curves in the xy-plane. In each case, find the particle’s velocityand acceleration vectors at the stated times, and sketch them asvectors on the curve. Motion on the parabola y = x2 + 1r(t) = ti + (t2 + 1)j; t = -1, 0, and 1
The angle between the velocity and acceleration vectors at time t=0 is
Suppose a > 0the vector function that describes the motion of a particle for t ≥ 0. Find the tangential and normal components of acceleration
A projectile of mass m is launched from an initial position r0 with an initial velocity v0. Find its position vector as a function of time.
Given a particle is moving in a curve r(t) = cos 6t i + sin 6t j + 10t k. Find the tangential component of its acceleration correct to two decimal places, at t = 3. Given a particle is moving in a curve r(t) = cos 6t i + sin 6t j + 10t k. Find the normal component of its acceleration correct to two decimal places, at t = 3.
In Exercises 5–8, r(t) is the position of a particle in the xy-plane at time t. Find an equation in x and y whose graph is the path of the particle. Then find the particle’s velocity and acceleration vectors at the given value of t.