Bank robbers have pushed a 1000 kg safe to a second story floor to ceiling window. they plan to break the window, then lower the safe 3.0 meteres to their truck. not being too clever, they stack up 500 kg of furnature, tie a rope between the safe and the furnature, and place the rope over the pully. then they push the safe out of the window. what is the saves speed when it hits the truck? the coefficient of kinetic friction between the furniture and the floor is 0.50.

Explanation with

First, in problems like this, it is always clear to draw a diagram to make sure you understand the problem.  If it is not possible to draw the diagram correctly, perhaps something is misunderstood or missing from the question.

Here, see the attached image.

Note that the rope has a tension of T that pulls both the furniture and the safe.

To find the final speed (when the safe hits the truck), we need first to find the acceleration.

The system's total mass, M = 1000+500 kg = 1500 kg

Forces acting on the system

= gravity acting on the safe less friction acting on the furniture.

= m1*g - mu*m2g

= 1000*9.81 - 0.5*500*9.81

= 7357.5 N

Acceleration, a = F/m = 7357.5 / 1500 = 4.905 m/s^2

Initial speed = 0 m/s

distance travelled, S = 3m

Let final speed = v

Kinematics equation gives

v^2-u^2 = 2aS

v^2 = 2*4.905*3 - 0^2 = 29.43 m^2/s^2

final speed, v = sqrt(29.43) = 5.4 m/s (to two significant figures.