Question

In the figure, a frictionless roller coaster car of mass m -828 kg tops the first hill with speed vo -17.0 m/s at height h 42.0 m. What is the speed of the car at (a) point A, (b) point B, and (c) point C? (d) How high will the car go on the last hill, which is too high for it to cross? Use g-10 m/s2 .4 lirst hill h/2

Answer 1

a)

By Conservation of energy at point A

(1/2)mV_o² +mgh =(1/2)mV_A²+mgh

(1/2)V_A²=(1/2)V_o²

V_A =V_o=17 m/s

b)

By Conservation of energy at point B

(1/2)mV_o² +mgh =(1/2)mV_B²+mg(h/2)

(1/2)*17²+10*42 =(1/2)*V_B² +10*(42/2)

V_B=26.627 m/s

c)

By Conservation of energy at point C

(1/2)mV_o² +mgh =(1/2)mV_C²+mg(0)

(1/2)*17²+10*42 =(1/2)*V_C²

V_C=33.6 m/s

d)

By Conservation of energy

(1/2)mV_o² +mgh =(1/2)mV²+mgH

at maximum height H=0

(1/2)*17²+10*42 =10*H

H=56.45 m