Question

Suppose that the experiment was performed with a ball launched at an initial velocity of 30 m/s. What should the distance (R) between the catapult and the bucket be so that the ball lands in the bucket? Note that the launch angle (θ) was 27.5°, the launch height (yi) was 9.59 m, and the height of the bucket opening (yf) was 2.5 m.

Answer 1

Q1.

Ans- initial velocity u_o =30m/s

        Let ball lands in the bucket at time t.

        then from equation-

          yf - yi =( u_o sin(theta)) t - gt^2 /2

          2.5 - 9.59 = (30* sin(27.8^o))t - 9.8 t^2 /2

          4.9 t^2 - 13.99 t -7.09=0

          t=3.294s

      Distance R between the catapult and bucket is -

             R= (u_o cos(theta)) t = (30* cos(27.8^o))*(3.294 ) =87.41m

So, Distance R between the catapult and bucket is 87.41m