The height above the ground at position 10m is 1

The answers are given below in the explanation.

Step-by-step explanation

(11) Given :

the kinetic energy of the cabinet at the bottom of the ramp = KE_bottom = 1701.75 J,

the mass of the cabinet = m = 100 kg.

Hence, the speed of the cabinet at the bottom of the ramp is :

v_f1 = √ ( 2 x KE_bottom / m )

= √ ( 2 x 1701.75 J / 100 kg )

= 5.83 m / s.

(12) Given :

the distance the cabinet travelled down the ramp = d = 10 m,

its initial speed down the ramp = u = 0 m / s,

the time it took the cabinet to go down the ramp = t = 2.1 s.

Therefore, the acceleration of the cabinet down the ramp is :

a = 2d / t²

= 2 x 10 m / ( 2.1 s )²

= 4.535 m / s².

Hence, the speed of the cabinet at the bottom of the ramp is :

v_f2 = u + at

= 0 m / s + 4.535 m / s² x 2.1 s

= 9.5 m / s.

(13) v_f2 / v_f1 = 9.5 / 5.83 ~ 1.6.

Hence, the final speed from #12 is almost 1.6 times the final speed from #11.

This difference comes because as the friction force is suddenly removed by clicking the " frictionless " button, and hence the cabinet accelerates at a faster rate to reach its final speed of 5.83 m / s.