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20 Vector Calculus

20 Vector Calculus - 20 VECTORCALCULUS 1 . .Find

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20. VECTOR CALCULUS 1. A golfer strikes a ball with initial velocity 18 i  + 20 j  metres per second where  i  is horizontal and  j  is vertical.  Throughout the flight of the ball the acceleration due to gravity is –10 j .  The point where the ball lands is at  the same height as the point from which it was struck.  Find (a) [2 marks] the velocity of the ball after  t  seconds __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (b)[2 marks] the position vector of the ball after  t  seconds __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (c) [1 mark] the initial speed of the ball __________________________________________________________________________________ __________________________________________________________________________________ (d)[3 marks] the horizontal distance the ball travels __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (e) [2 marks] the maximum height reached by the ball. VET Calculus 124 20. Vector Calculus

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__________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET Calculus 125 20. Vector Calculus
2. A particle,  P , is moving in a horizontal plane.  Its acceleration at any time,  t , is  sin  t   i  + 2 cos  t   j .  At time  t  = 0 the particle is at the point (0, -2) moving with velocity – i .  Find expressions  for (a) [3 marks] the velocity at time  t . __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (b)[3 marks] the position at time  t . __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (c) [1 mark] the speed at time  t . __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET Calculus 126 20. Vector Calculus

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(d)[6 marks] the minimum distance from the origin and the maximum distance from the origin. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (e) [5 marks] If the position vector of  P  is given by  x   i  +  y j  find values of  a  and  b  such that  1 2 2 2 2 = + b y a x What sort of curve is this?  State whether
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