Free Physics resources · VCE Units 3 & 4
A full VCAA-style practice paper with a marking guide, plus original practice questions and a study planner — sent straight to your inbox.
A satellite orbits Earth in a circular orbit at an altitude of 2.0 x 10^7 m above the surface. Take Earth's mass as 5.97 x 10^24 kg, Earth's radius as 6.37 x 10^6 m, and G = 6.67 x 10^-11 N m^2 kg^-2. (a) Calculate the orbital radius. (b) Calculate the satellite's orbital speed. (c) Calculate the orbital period in hours.
(a) 1 mark: r = R + h = 6.37 x 10^6 + 2.0 x 10^7 = 2.637 x 10^7 m. (b) 2 marks: 1 mark for equating gravitational force to centripetal force, GMm/r^2 = mv^2/r, giving v = sqrt(GM/r); 1 mark for v = sqrt(6.67 x 10^-11 x 5.97 x 10^24 / 2.637 x 10^7) = 3.89 x 10^3 m s^-1 (accept 3.9 x 10^3). (c) 2 marks: 1 mark for T = 2(pi)r/v = 2(pi)(2.637 x 10^7)/3886; 1 mark for T = 4.26 x 10^4 s = 11.8 hours (accept 11.8 to 11.9). Total: 5 marks.
A ball is launched from ground level at 25 m s^-1 at 30 degrees above the horizontal. Ignore air resistance and take g = 9.8 m s^-2. (a) Find the horizontal and vertical components of the initial velocity. (b) Find the maximum height reached. (c) Find the horizontal range.
(a) 2 marks: 1 mark for ux = 25 cos30 = 21.7 m s^-1; 1 mark for uy = 25 sin30 = 12.5 m s^-1. (b) 2 marks: 1 mark for using v^2 = uy^2 - 2gH with v = 0, so H = uy^2/(2g); 1 mark for H = 12.5^2/(2 x 9.8) = 7.97 m (accept 7.9 to 8.0 m). (c) 2 marks: 1 mark for time of flight t = 2uy/g = 2 x 12.5/9.8 = 2.55 s; 1 mark for range = ux x t = 21.7 x 2.55 = 55.2 m (accept 55 to 55.3 m). Total: 6 marks.
More to practise: all Physics practice questions.