Isaac Newton sat under an apple tree to drink some tea and think. While he was thinking, an apple fell off a branch of the tree. The equation \( v=(19.8 d)^{\frac{1}{2}} \) can be used to find the velocity \( v \), in meters per second, of the apple after dropping a distance \( d \), in meters. If the apple was connected to a branch 4 meters above the ground, what was the velocity of the apple, to the nearest hundredth, when it hit the ground? Answer

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.

157. Una bombola a pareti rigide di 30 L contiene \( 0,5 \mathrm{moli} \) di un gas perfetto biatomico alla temperatura iniziale di \( 20^{\circ} \mathrm{C} \). Essa viene tenuta sotto il sole per un certo tem- po e si nota che la temperatura finale è di \( 80^{\circ} \mathrm{C} \). Trascu- rando la dilatazione termica della bombola, si calcoli: - il lavoro fatto dal gas; - la variazione di pressione del gas; - la variazione di energia interna del gas. [0 J; \( \left.8,3 \times 10^{3} \mathrm{~Pa} ; 6,2 \times 10^{2} \mathrm{~J}\right] \) (Esame di Fisica, Corso di laurea in Farmacia, Università La Sapienza di Roma, 2006/2007)

An object of mars 5.0 kg moves around a aincle of radius 6.0 m coith a constant speeds of 10 . om/s. Calc-te 1 . angular velocity Centripetal force on the body

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.