Question

3. A small child is sitting in a high chair eating and throwing Cheerios. She can launch each Cheerio with a maximum initial speed of 2.00 m/s in any direction and her hand is 1.00 m above the floor as she does so. What is the minimum area of the floor that her father needs to sweep in order to be certain to collect all the Cheerios when she is done eating? (Assume that the Cheerios do not bounce on landing, but rather stick to the juice-covered floor.)

Answer 1

Step 1 Maximum range is achieved when tossed at 45 degree Step 2 time of flight = ? use 2 nd equation of motion for vertical component of velocity u = 2 sin 45^dergee = squareroot 2 d = -1 m a = -g = -9.8 d = u t + 1/2 a t^2 = > - 1 = squareroot 2 t - 0.5 times 9.8 times t^2 Solving this quadratic we get t = 0.6185 S Step 3 R = (2 cos 45) t = squareroot 2 times 0.6185 m = 0.8747 m Area = pi R^2 = pi times (0.8747)^2 = 2.403 m^2

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