The minute hand of a wall clock measure 11.3cm from axis to tip. what is the dispacement vector of its tip (a)from a quarter after the hour to half past (b)in the next half hour and (c)in the next hour?

.(c) In the next hour, the minute hand would have move by 60 min thereby reaching the same position as it was initially. Therefore the net displacement of the minute hand is zero.The displacement vector in this case would be .Therefore the displacement vector of the minute hand is 22.6 cm  from above to get displacement vector as:andSubstitute the value of vectors ) of the minute hand clock is given as:The displacement vector (say  as:Substitute the given value of b to obtain vectoris given as:However the minute hand has now moved by half hour or 30 minutes which is equal to the rotation by 180° clockwise.Therefore vector as:Substitute the given value of to obtain vector  remains the same, that is:With the same reference position of the minute hand, the vector.(b) The minute hand position when it has moved by 30 min relative to the initial position is shown below:Therefore the displacement vector of the minute hand is  from above to get displacement vector as:Substitute the value of vectors)of the minute hand clock is given as:The displacement vector (say  as:Substitute the value of b to solve for vectorThe negative sign highlight the fact that the rotation of minute hand is clockwise relative to its initial position, which itself was defined at angle 90° from positive x axis, measured clockwise (refer figure below).The quarter after hour to hour past, the minute hand would have displaced by15 minutes (rotation by ), therefore the position vector of the minute hand can be written as: becomes:The negative sign is due to the fact that the angle made by the minute hand from positive axis is measures clockwise.Substitute the given value of a , the vector can be written as:The position vector respectively.Given:a = 11.3 cmb = 11.3 cm(a) The quarter after hour to half past represents the displacement of the minute hand, which is by 15 minutes. This can be seen from the fact that the quarter after hour represents 15 minutes after an hour and the half past represent 30 min. Therefore the elapsed time is 15 minutes.If the motion of the minute hand is represented on the Cartesian coordinate such that the origin represents the center of the clock, the minute hand can be represented on it.We assume that, initially, the minute hand subtended angle -90° from positive x axis, measured clockwise (refer figure below)._y and b_xrepresents its position vector. The magnitude of the position vector is given by b whereas the horizontal and the vertical component of the vector is b respectively.When the minute hand displaces from the initial position to come at final, the vector_y and a_x. The magnitude of the position vector is given by a whereas the horizontal and the vertical component of the vector is aAssumptionsLet us assume that the position vector for the tip of the minute hand of the wall clock, at initial position is given by vector