Can you just give a brief description of equation of projectile motion?

Asked by venkatakrishnan.subramaniam | 30th Sep, 2015, 07:07: PM

Expert Answer:

begin mathsize 12px style In space projectile space motion space object space covers space horizontal space distance space due space to space horizontal space velocity space and space vertical space downwards space distnace space due space to space vertical space velocity. The space Motion space along space straight x space axis colon Since space the space velocity space of space an space object space in space the space horizontal space direction space is space constant comma space so space the space accelration space straight a subscript straight x space in space the space horizontal space direction space is space zero. The space position space of space the space object space at space any space time space straight t space along space horizontal space direction space is space given space by comma straight x space equals space straight x subscript 0 plus straight u subscript straight x straight t plus 1 half straight a subscript straight x straight t squared space straight x subscript 0 equals 0 comma space straight u subscript straight x space equals space ucosθ space and space straight a subscript straight x space equals space 0 rightwards double arrow space straight x space equals space ucosθ space straight t rightwards double arrow straight t space equals space straight x over ucosθ space space space space space left parenthesis straight i right parenthesis The space Motion space along space straight y space axis colon Since space the space velocity space of space an space object space in space the space space vertical space direction space decreasing space due space to space gravity comma space so space the space accelration space straight a subscript straight y space equals negative straight g. The space position space of space the space object space at space any space time space straight t space along space vertical space direction space is space given space by comma straight y space equals space straight y subscript 0 plus straight u subscript straight y straight t plus 1 half straight a subscript straight y straight t squared space straight y subscript 0 equals 0 comma space straight u subscript straight y space equals space usinθ space and space straight a subscript straight y space equals space minus straight g straight y space space equals space straight u space sin space θt space minus space 1 half gt squared space space space space left parenthesis ii right parenthesis Equation space left parenthesis iii right parenthesis space is space in space the space form space of straight s space equals space ut space plus 1 half gt squared straight u space equals space straight u space sin space straight theta By space substituing space eq space left parenthesis straight i right parenthesis space in space left parenthesis ii right parenthesis space we space get straight y space equals space usinθ open parentheses straight x over ucosθ close parentheses space minus space open parentheses 1 half fraction numerator straight g over denominator straight u squared cos squared straight theta end fraction close parentheses straight x squared space space The space equation space of space the space path space of space straight a space projectile space is space given space as comma straight y space equals space straight x space tanθ space minus space open parentheses 1 half fraction numerator straight g over denominator straight u squared cos squared straight theta end fraction close parentheses straight x squared space space space space space space tanθ space equals space usinθ over ucosθ This space equation space gives space the space path space of space projectile space projected space at space some space angle space with space the space horizontal space direction space from space ground space is space parabolic space path. straight y space equals space αx space minus space βx squared straight alpha space equals space tanθ straight beta space equals open parentheses 1 half fraction numerator straight g over denominator straight u squared cos squared straight theta end fraction close parentheses space end style

Answered by Priyanka Kumbhar | 1st Oct, 2015, 12:51: PM