A block of mass M travels horizontally with a constant speed v0 on a plateau of

Question

A block of mass M travels horizontally with a constant speed v0 on a plateau of height H until it comes to a cliff. A toboggan of mass M2 is positioned on level ground below the cliff as shown. The center of the toboggan is a distance D from the base of the cliff.

a) Determine D in terms of v0, H, and g so that the block lands in the center of the toboggan.

b) The block sticks to the toboggan, which is free to slide without friction. Determine the resulting velocity of the block and toboggan

Explanation / Answer

(a)

D = v0*t

apply second equation of motion,

H = u*t + (1/2)*g*t

(u = 0)

t = sqrt(2*H / g)

so, D = v0*sqrt(2*H / g)

(b)

let,

resulting velocity of the block and toboggan = v

apply conservation of momentum in the horizontal direction,

M*v0 = (M + M2)*v

v = M*v0 / (M + M2)

answer

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