Show, by differentiating components, that (a)

d

dt

(A · B) =

dA

dt

· B + A ·

dB

dt
(b)

d

dt

(A × B) =

dA

dt

× B + A ×

dB

dt

,

just like the derivative of the product of two algebraic functions​

The man of mass m1 and the woman of mass m2 are standing on opposite ends of the platform of mass m0 which moves with negligible friction and is initially at rest with s = 0. the man and woman begin to approach each other. derive an expression for the displacement s of the platform when the two meet in terms of the displacement x1 of the man relative to the platform.

In addition to gravity, what is the other predominant force that affects the motion of a pendulum?

The first law of thermodynamics is as follows: ∆u=q-w , which means in a system is equal to added, minus done by the system. the units for these variables are in .