Given position of particle one at time t as , as
This equation represents equation of the ellipse. Position of particle two at time t as ,
This equation represents equation of the circle with unit radius. We can see path taken by particle one and particle two in the above graph. |
a. When two paths intersect, at the point of intersection and . But the time of intersection need not be same. From graph we can see that there are two points of intersection at and . Number of intersection points= 2. |
b. The collision points are the points of intersection when and at same time. This means that not only the path intersects but both particles meet.
Multipy equation by 2. Add it to equation At , particles collide. Substitute in and to get the collision point at time .
The collision point is Number of collision point =1. |
c. The collision point at time is First collision point: (x,y) = Second collision point: (x,y) = Third collision point: (x,y) = |
d. Now position of particle two at time t as , , This equation represents equation of the circle with unit radius. From graph we see that there are two points of intersection at and . Number of intersection points= 2. |
e. For collision point consider
Multipy equation by 2. Add it to equation But There is no point of collision. Number of collision point =0. |
(10 points) Suppose that the position of one particle at time t is given by x1...
need help Suppose that the position of one particle at time t is given by and the position of a second particle is given by 22 3+cos(t), v2 1+sin(t), 0st s 2r. (a) How many points of intersection are there for these paths? Number of intersection points- (b) How many of these points of intersection are collision points? In other words, how many times are the particles in the same place at the same time? Number of collision points (c...
1. Suppose that the position of one particle at time t is given by x1= 3 sint yı = 2 cost 0<1<21 and the position of a second particle is given by x2 = -3+ cost y2 = 1+ sin 1 0<t<21 (a)Graph the paths of both particles. How many points of intersection are there? (b) Are any of these points of intersection collision points? In other words, are the particles ever at the same place at the same time?...
Suppose that the position of one particle at time t is given by the equations Xy and y1. Meanwhile, the position of a second particle is given by the equations 2 and Y2 X1 - 3sin() Yi - 2cos(t) Osts 21 2-3 + cos(0) Y2 - 1 + sin(1) Osts 2x (a) Graph the paths of both particles. (Do this on paper. Your instructor may ask you to turn in this work.) How many points of intersection are there? (b)...
Suppose that the position of one particle at time t is given by Xi= 3 sint Yi = 2 cost 0 < t < 211 and the position of a second particle is given by X2 = -3+ cost y2 = 1+ sin t 0<t<21 (a)Graph the paths of both particles. How many points of ntersection are there? (b) Are any of these points of intersection collision points? In other words, are the particles ever at the same place at...
Suppose that the position of particle 1 at time t is given by x_1 = 2 sin t. y_1 = 7 cost. 0 lessthanorequalto t lessthanorequalto 2 pi, and the position of particle 2 at time t is given by x_2 = -4 + cos t. y_2 = 9 + sin t. 0 lessthanorequalto t lessthanorequalto 2 pi. Find the maximum number of points of intersection of the paths of the two particles. Choose the answer from the following: 0...
Suppose that the position of one particle at time t is given by y1-2 cost), x,-4 sin(t), ostsZr and the position of a second particle is given by 4 (a) Graph the paths of both particles. We were unable to transcribe this image Suppose that the position of one particle at time t is given by y1-2 cost), x,-4 sin(t), ostsZr and the position of a second particle is given by 4 (a) Graph the paths of both particles.
3. (i) Find the kinetic energy of a particle of mass m with position given by the coordinates (s, u, v), related to the ordinary Cartesian coordinates by y z = 2s + 3 + u = 2u + v = 0+03 (ii) Find the kinetic energy of a particle of mass m whose position is given in cylindrical coordinates = = r cos r sine y (iii) Find the kinetic energy of a particle of mass m with position...
3. (10 total points) A particle travels along the intersection of (2) 1z=x+y (a) (2 points) Write the path of particle as a vector might find cos2(t)+ sin? (t) = 1 useful. function r(t) =< x(t),y(t), z(t) > of t. Hint: you (b) (4 points) Find the equation of the tangent plane of z = x+y at (1,3). (c) (4 points) Find the tangent line of the particle path at the point (1,0,1). 3. (10 total points) A particle travels...
I need help with B, C, D. These are Calc 3 problems 32. Suppose a particle of mass m has position given by r(0) =< 1,0,0 >, and velocity given by v(0)0,1,-1 > at time t = 0. Also, assume that for every time t 20 the particle experiences only the force given by the vector function F(t) = m < -cos(t), 0, sin(t) >. Disregard units in this problem a) Use Newton's Second Law, F(t) = ma(t) (where a(t)...
calculus 3 8. The position of a particle moving in a circular path is given by r(t) =< -4 sin(3t), 4 cos(3t) >. Find the speed v of the particle at any time t.