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Trigonometry (MindTap Course List)

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Additional Topics In Trigonometry

Section3.3: Vectors In The Plane

Problem 11ECP

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A projectile starts at time t = 0 at the point (6, 6, 15) with the initial velocity of (8, 10, 10). Assuming that the force of gravity is (0, 0, -10) and there is a
wind that pushes the projectile with the force of (2, 4, 0), let (A, B, 0) be the coordinates of the point where the projectile lands on the xy-plane.
Find A =
P, B =

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Let vector r(t) = <5sin(t), 5cos(t), 2t^(3/2)> be the position function of an object.a. Find vector v(t) and vector a(t), the velocity and acceleration of the object.b. Find the speed of the object.c. Find the distance the object travels on the interval [0, 1]. Also find the average speed of theobject on this interval.
The force exerted by an electric charge at the origin on a charged particle at the point (x,y,z) with position vector KF F = is F (F) = where K is constant. Assume K = 25. Find the work done as the particle moves along a straight line from (3,0,0) to (3,5,2)
Brazilian soccer star Marta has a penalty kick in the quarter-final match. She kicks the soccer ball from ground level with the (x, y)-coordinates (76, 21) on the soccer field shown in the figure and with initial velocity vo = 8i - 4j+23k ft/s. Assume an acceleration of 32 ft/s² due to gravity and that the goal net has a height of 8 ft and a total width of 24 ft. 105 ft 1 105 ft r₁ = rj = rk = 165 ft Determine the position function that gives the position of the ball t seconds after it is hit. (Use symbolic notation and fractions where needed.) r(t) = ri(t)i + rj(t)j + rk(t)k Incorrect 81+76 -41+21 ↓ 23r+1672² 165 ft 12 12
A projectile is fired northward from a height of 420 m. Assuming that the x-axis is pointing east, O representing ground level. The projectile's y-axis is pointing north and the z-axis is pointing up with z = initial velocity vector is v(0) = (0, 99, 22). In addition to a downward gravitational acceleration of 9.8 m/s², it experiences in flight an westward acceleration of 5 m/s² due to the wind. Find the projectile's velocity and position vectors t seconds after the projectile is fired.
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Brazilian soccer star Marta has a penalty kick in the quarter-final match. She kicks the soccer ball from ground level with the (x, y)-coordinates (76, 21) on the soccer field shown in the figure and with initial velocity vo = 8i - 4j+23k ft/s. Assume an acceleration of 32 ft/s² due to gravity and that the goal net has a height of 8 ft and a total width of 24 ft. 105 ft 105 ft ri = rj = 165 ft rk = e 165 ft Determine the position function that gives the position of the ball t seconds after it is hit. (Use symbolic notation and fractions where needed.) r(t) = r(t)i + r(t)j +rk(t)k 12 12 X
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WHICH ANSWER IS CORRECT? Given the curve C parametrized by the vector equation r⃗ (t)=3sin(t)i^+[2−sin(t)+cos(t)]j^−3cos(t)k^,t∈[0;2π] The given curve C has the property that A. Its tangent vector and acceleration vector are always orthogonal. B. The cross product between the tangent vector the acceleration vector always equals −3i^+9j^−3k^. C. The cross product of its acceleration vector and its tangent vector is always parallel to i^+3j^+k^. D. Its vector function is nowhere orthogonal to its tangent vector. E. None of the listed alternatives.
the position vector r describes the path of an object moving in space. (a) Find the velocity vector, speed, and acceleration vector of the object. (b) Evaluate the velocity vector and acceleration vector of the object at the given value of t. r(t) = ⟨t, −tan t, e^t⟩ t = 0
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3. The position vector of a particle moving in the plane is given by r(t) =e 'i+e'j. a) Find the velocity, acceleration, and speed at an arbitrary time t. b) Sketch the path of the particle together with the velocity and acceleration vectors at time t = 0. Sketch your graph and vectors clearly, labeling all that is relevant.
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