A hollow cyllinder is given a velocity of \( 4.2 \mathrm{~m} / \mathrm{s} \) and rolls up an incline to a height of 1.80 m . If a hollow sphere of the same mass and radius is given the same initial velocity, how high (in m ) does it roll up the incline? (Assume both objects roll without slipping.) Additional Materials Reading

5. Qué energía potencial posee un objeto con una masa de 6 kg a. A 4 m del suelo. b. A 6 m del suelo. 6. ¿A qué altura debería situarse una masa de 2 kg para poseer una energía

9. Si dejamos caer al suelo una piedra cuya masa es de 4 kg desde una altura de 4 m , ¿Cuál es la energía cinética cuando ya ha recorrido la mitad de la caída a) hacia el suelo? b) CCual es la velocidad cuando alcanza el suelo?

5.3 An aeroplane accelerates uniformly such that it goes from rest to \( 144 \mathrm{km.hr}^{-1} \) in 8 s . Calculate 5.3 .1 the acceleration of the aeroplane. 5.3 .2 the total distance that it has travelled in this time. Total for qu

7.2 A beam of light travels from water to plastic. The speed of light in plastic is \( 2,05 \times 10^{8} \mathrm{~m} \cdot \mathrm{~s}^{-1} \). The refractive index of water is 1,33 . Calculate the refractive index of plastic.

QUESTION 6 (Start on a new page.) It has been established that the planet Omega has a moon and that the moon of Omega orbits the planet at a height, above the surface of Omega, which is equal to twice the radius of Omega. The mass of planet Omega is \( 3 \times 10^{15} \mathrm{~kg} \) and the mass of its moon is \( 1.5 \times 10^{13} \mathrm{~kg} \). The radius of the planet Omega is \( 8.5 \times 10^{6} \mathrm{~m} \) and the radius of its moon is \( 2.5 \times 10^{5} \mathrm{~m} \). 6.1 Determine the distance between the centre of the planet Omega and the centre of its moon.