Question

A block of mass M₁ travels horizontally with a constant speed v_o 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 v_o  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.

Answer 1

(a) Projectile methods. Find t in y direction. d_y = v_iyt + ½ at² 

t = √(2H/g)

D is found with v_x = d_x/t D = vot  v_o√(2H/g)

(b) Apply momentum conservation in the x direction. 

p_before(x) = p_after(x) M₁v_o = (M₁ + M₂)v_f 

v_f = M₁v₀/(M₁ + M₂)