An ant is moving around the unit circle in the plane so that its location is...
An ant is moving around the unit circle in the plane so that its location is given by the parametric equations (cos(π t), sin(π t)). Assume the distance units in the plane are "feet" and the time units are "seconds". In particular, the ant is initially at the point A=(1,0). A spider is located at the point S=(3,0) on the x-axis. The spider plans to move along the tangential line pictured at a constant rate. Assume the spider starts moving at the same time as the ant. Finally, assume that the spider catches the ant at the tangency point P the second time the ant reaches P. (a) The coordinates of the tangency point P=( Incorrect: Your answer is incorrect. , $$ Correct: Your answer is correct. sqrt(3**2-1)/3). (b) The FIRST time the ant reaches P is seconds. (c) The SECOND time the ant reaches P is seconds. (d) The parametric equations for the motion of the spider are: x(t)= t + ; y(t)= t + .
Can you please do it with out using derivatives?
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An ant is moving around the unit circle in the plane so that its
location is...
An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t), so it's location...
An object is moving around the unit circle with parametric
equations x(t)=cos(t), y(t)=sin(t), so it's location at
time t is P(t)=(cos(t),sin(t)) . Assume 0
< t < π/2. At a given time t, the tangent line
to the unit circle at the position P(t) will determine a
right triangle in the first quadrant. (Connect the origin with the
y-intercept and x-intercept of the tangent
line.)
(a) The area of the right triangle is
a(t)= .
(b)
lim t →
pi/2−a(t)=
...
An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t), so it's location...
An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t), so it's location at time t is P(t)=(cos(t),sin(t)) . Assume 0 < t < ?/2. At a given time t, the tangent line to the unit circle at the position P(t) will determine a right triangle in the first quadrant. (Connect the origin with the y-intercept and x-intercept of the tangent line.)
I just need help with question F An object is moving around the unit circle with...
I just need help with question F
An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t), so it's location at time t is P(t)=(cos(t), sin(t)). Assume 0 < t < pi/2. At a given time t, the tangent line to the unit circle at the position P(t) will determine a right triangle in the first quadrant. (Connect the origin with the y-intercept and x-intercept of the tangent line.) The identity sin(2t)=2sin(t)cost(t) might be useful in some...
(a) The velocity of a particle moving in the x - y plane is given by...
(a) The velocity of a particle moving in the x - y plane is given by ☺ = ((-3.2t+ 9.6 t)i + (2.4t + 4.0)j) m/s, where v is in meters per second and t in seconds. The particle is at the origin of the coordinate system at t = 0 s. i. Determine the magnitude of the acceleration of the particle at t = 2.5 s. ANS: ii. Determine the position of the particle at t = 2.5 s....
2. Consider a mass m moving in R3 without friction. It is fasten tightly at one...
2. Consider a mass m moving in R3 without friction. It is fasten tightly at one end of a string with length 1 and can swing in any direction. In fact, it moves on a sphere, a subspace of R3 1 0 φ g 2.1 Use the spherical coordinates (1,0,) to derive the Lagrangian L(0,0,0,0) = T-U, namely the difference of kinetic energy T and potential energy U. (Note r = 1 is fixed.) 2.2 Calculate the Euler-Lagrange equations, namely...
I need the answers with steps please! 10. A boy throws a ball with an initial...
I need the answers with steps please!
10. A boy throws a ball with an initial velocity of 25 m/s at an angle of 30° above the horizontal. If air resistance is negligible, how high above the projection point is the ball after 2.0s? How long is it in the air, and how far does it go before hitting the ground? 11. A projectile leaves the ground at 150 m/s and reaches a maximum height of 0.57 km. If there...
5:16 lLTE ) Done 1 of 5 Assessment #1 (Kinematics of a Particle) Rectilinear Motion (Straight...
5:16 lLTE ) Done 1 of 5 Assessment #1 (Kinematics of a Particle) Rectilinear Motion (Straight linc Motion 3. The position of a point during the interval of time from r otor 6 is given by ** * m. (a) What is the maximum velocity during this interval of time, and at what time does it occur? (b) What is the acceleration when the velocity is a maximum? (20 m/s, 0 m/s 3. A test projectile is fired horizontally into...
An object is moving around the unit circle with parametric
equations x(t)=cos(t), y(t)=sin(t), so it's location at
time t is P(t)=(cos(t),sin(t)) . Assume 0
< t < π/2. At a given time t, the tangent line
to the unit circle at the position P(t) will determine a
right triangle in the first quadrant. (Connect the origin with the
y-intercept and x-intercept of the tangent
line.)
(a) The area of the right triangle is
a(t)= .
(b)
lim t →
pi/2−a(t)=
...
I just need help with question F
An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t), so it's location at time t is P(t)=(cos(t), sin(t)). Assume 0 < t < pi/2. At a given time t, the tangent line to the unit circle at the position P(t) will determine a right triangle in the first quadrant. (Connect the origin with the y-intercept and x-intercept of the tangent line.) The identity sin(2t)=2sin(t)cost(t) might be useful in some...
(a) The velocity of a particle moving in the x - y plane is given by ☺ = ((-3.2t+ 9.6 t)i + (2.4t + 4.0)j) m/s, where v is in meters per second and t in seconds. The particle is at the origin of the coordinate system at t = 0 s. i. Determine the magnitude of the acceleration of the particle at t = 2.5 s. ANS: ii. Determine the position of the particle at t = 2.5 s....
2. Consider a mass m moving in R3 without friction. It is fasten tightly at one end of a string with length 1 and can swing in any direction. In fact, it moves on a sphere, a subspace of R3 1 0 φ g 2.1 Use the spherical coordinates (1,0,) to derive the Lagrangian L(0,0,0,0) = T-U, namely the difference of kinetic energy T and potential energy U. (Note r = 1 is fixed.) 2.2 Calculate the Euler-Lagrange equations, namely...
I need the answers with steps please!
10. A boy throws a ball with an initial velocity of 25 m/s at an angle of 30° above the horizontal. If air resistance is negligible, how high above the projection point is the ball after 2.0s? How long is it in the air, and how far does it go before hitting the ground? 11. A projectile leaves the ground at 150 m/s and reaches a maximum height of 0.57 km. If there...
5:16 lLTE ) Done 1 of 5 Assessment #1 (Kinematics of a Particle) Rectilinear Motion (Straight linc Motion 3. The position of a point during the interval of time from r otor 6 is given by ** * m. (a) What is the maximum velocity during this interval of time, and at what time does it occur? (b) What is the acceleration when the velocity is a maximum? (20 m/s, 0 m/s 3. A test projectile is fired horizontally into...
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