Motion along a line? Two objects move along? the x ? -axis with position functions x 1t) = 2sin tand x 2t) = sin (t ? 2. At what times on the interva? l [0, 2??]are the objects closest to each other and farthest from each other?

Solution Step 1 In this problem it is given that two objects move along the x-axis with position functions x 1t) = 2sin tand x 2t) = sin (t 2). we have to find at what times on the interval [0,2]does the objects are closer to each other and farther to each other. Step 2 We have x (1) = 2sin tand x (t2 = sin (t )2 In order to find the time of closest point we have to equate the position functions of two objects. x (t) = x (t) 1 2 2 sin t = sin (t ) 2 2 sin t = sin ( 2t) We know that sin(90 ) = cos that is sin( 2) = cos Thus we get 2 sin t = cos t cos t 2 tan t = 1 2 t = tan ( )1 2 1 1 Calculating the value of tan ( ) 2n calculator we get, o t = 26.56 o ut the given interval for t is [0, ]. Clearly t = 26.56 / [0,2] Thus the two objects will not come closer to each other in the given interval.