Pls solve question no. 12

Pls solve question no. 12 • ' ••n•CBSE.PH.KM.75 11. The position vector ofa panicle varies with time t as x = kt(l- at), where k is a constant vectorandu (a) the velocity v and the acceleration a of the particle as functions of lime. (b) the time interval At taken by the particle io return to the initial points, and the distance covered during that time. A balloon starts rising from the surface of the Earth. The ascent rate is constant equal to vo. Due to the wind the balloon gathers the horizontal velocity component = ay, where a is a constant and y is the height of ascent. Find how the following quantities depend on the height ofascent. (a) The horizontal drift of the balloon x(y); (b) The total, tangential, and normal accelerations of the balloon. 13. Two boats A and B move away from buoy anchored at the middle of a river along mutually perpendicular straight lines, the boat A along the river and the boat B across the river Having moved Off an equal distance from the buoy the boat returned. Find the times of motion of boats tA/ tn if the velocity of each boat with respect to water is n times greater than the stream velocity A ball starts falling with zero initial velocity on a smooth inclined plane forming an angle u with the

Dear Student,

v e r t i c a l c o m p o n e n t v_{y} = v_{0} h o r i z o n t a l c o m p o n e n t v_{x} = a y . i n t i m e t a c s e n t i s y = v_{0} t \frac{d x}{d t} = a y \frac{d x}{d t} = a v_{0} t x = \int_{0}^{t} a v_{0} t . d t = a v_{0} \times \frac{t^{2}}{2} t h a t s t h e h o r i z o n t a l d r i f t . t h e a c n n w i l l b e o n l y i n h o r i z o n t a l d i r e c t i o n . a s t h e v e r t i c a l v e l o c i t y i s c o n s \tan t . a_{x} = \frac{d^{2}}{d t^{2}} (a v_{0} \times \frac{t^{2}}{2}) = a v_{0} R e g a r d s