a) What is the basketball\'s speed Vi the instant it leaves the ramp? Write the

Question

a) What is the basketball's speed Vi the instant it leaves the ramp? Write the result in terms of the given quantities (yo and/or yi) and, perhaps, constants (e.g., g, pi, 1/2 ...).

Starting from distance yo above the ground, a basketball rolls without slipping down a ramp as shown in the drawing. The ball leaves the ramp vertically with a center-of-mass speed wi when it is a distance yi above the ground. Treat the ball as a uniform spherical shell (hollow sphere). Ignore air resistance. a) What is the basketball's speed vi the instant it aves the ramp? write the result in terms of the given b) What maximum height H above the ground does the ball travel? Write the result in terms of the given quantities (yo and/or y) and, perhaps, constants (e.g. g, T,Vi c Explain why H yousing correct physics principles. d) Determine numerical values for vi and H if yo 2.00 m and yr-0.95 m HINT: You can assume the basketball has a mass M and a radius R, but the final answers should not include either! ANOTHER HINT: Do the units work? If not, then something went wrong!

Explanation / Answer

a) from conservation of energy

k1+u1 = k2+u2

mgy0 = 1/2mvi^2+mgy1

1/2mvi^2 = mg(y0-yi)

vi = sqrt(2g(yo-y1)

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