A frictionless toy car is placed on a ramp, which is inclined at an unknown angle with respect to the horizontal. Starting from rest, the car is allowed to roll freely down the ramp. After a time interval of Δ=0.67 s, the car has traveled a distance of =1.2 m down the ramp and is moving with speed f. Find the speed of the car at the end of the 0.67 s time interval.

Amerry-go-round of radius r, shown in the figure, is rotating at constant angular speed. the friction in its bearings is so small that it can be ignored. a sandbag of mass m is dropped onto the merry-go-round, at a position designated by r. the sandbag does not slip or roll upon contact with the merry-go-round. how would you rank the following different combinations of m and r on the basis of the angular speed of the merry-go-round after the sandbag "sticks" to the merry-go-round from largest to smallest. a) m = 10kg, r = 0.25r b) m = 20kg, r = 0.25r c) m = 10kg, r = 0.50r d) m = 10kg, r = 1.0r e) m = 15kg, r = 0.75r f) m = 40kg, r = 0.25r