Question

7) A baseball player throws a baseball with an initial speed of 160 feet per second at angle of 27 to the horizontal. The ball leaves his hand at a height of 7 feet. a. Find the parametric equations that describe the position of the ball as a function of time. 6 pts b. Which equation would be used to find how long the ball was in the air, X(t) or y(t)? Explain your answer. (Do not solve) 4 pts c. Which equation would be used to find the maximum height of the ball, x(t) or y(t)? Explain your answer. (Do not solve) 4 pts d. Which equation would be used to find the horizontal distance that the ball has traveled, x(t) or y(t)? Explain your answer. (Do not solve) 4 pts

Answer 1

Given 7 initial speed, U = 160 ft I see. Angle with horizontal, ata x=27° Initial Height 7 feet we ولی، ہم K U cos a 2 horizontal velocity = =2 dx = ucosa JE x= Cucosa) t+ c at t=02 x = 0 >) o=o+C. =) ( =0

So x= (ucosa) t- Now On the vertical, accesoration of g (acc. due to gravity acts on ball so dy -g dt² dy -gt +(2 dt Now at too, velocity at too a do = usina It F0 so Usina = 0+(2 C2 = Usina dy Usina - gt dt y = (usinat gt² +63 Now at t=0, y = H = 7 ft H o-ot, = 3 = H 2 So (usin er) t- 1 gt +H- H=7 a) are dow 160 ft /sees X = 27°, from 1 and ② parametric equations X(t)= (160 (0827° ) + (160 sin 27°) + - 1 gt² + 7 y (t) = (160 sin 27°) +- 16.08742+7 ( we used ge 32.174 ft /se] 2

air upto the b) Since hall remains tine when in the y (t) to so use the time y (+) = 0 equation to find when ball reverina in cir. as y lt)=0 y (t)=0, bal bal reaches reaches ground Since ie (160 sin 270) + 16.087 t’+7 cs In order to find maximum height of yH) ball we will use y (t) = Heco(160 sin2r) t- 16.087t² +7=0 we will maximise above esnation to get max. height d) use an Order to find horizontal distance Travelled ky ball It) - - (160 connot But in order to find t we also have to have to use yl)-0 and find t the time of flight To find horizontal distance will have to use both equations rain emphasis on x6(160 (N9220) + to get final result.