Aparticle with charge − 5.20 nc is moving in a uniform magnetic field b⃗ =−( 1.24 t )k^. the magnetic force on the particle is measured to be f⃗ =−( 4.00×10−7 n )i^+( 7.60×10−7 n )j^. a calculate the x-component of the velocity of the particle.

b calculate the y-component of the velocity of the particle.

c calculate the scalar product v⋅f

d what is the angle between v and f ? give your answer in degrees.

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