H Answers are in notes to slide 2

5 13 1 9 17 6 14 2 10 18 H 7 15 3 11 19 8 16 Answers: 5a/2 (June 2006 Q 4(a)(i)) 4 N (January 2008 Q 1(b)) 25.6 ms-1 (velocity: 8i + 24.32j) 52 cm 1/8 96 2/3 N 5156 J 41.6° (M2 Ex 5D Q 3a) 2000 kg 4a/3 (June 2006 Q 4(a)(ii)) 1.0004 (1.00035…) 45 cm (June 2007 Q5) -100 m 2/3 s 0.414 s 25° 77.2° (velocity 10/3i + 14.7j) 4.14 ms-1 (a = 7g/16) 1/15 < e ≤ 1 38i + 15j 4 12 20

BACK TO THE BLOCKBUSTER GRID 1 Find the distance of the centre of mass from AB C (6m) D (2m) 2a 3a Each rod has mass m A B BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 2 A parcel of mass 2.5 kg is moving at 8 m s-1 on a smooth surface. It is brought to rest in 20 m by a force R. Find the value of R. BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 3 A ball is projected with velocity (pi + qj) m s-1 at angle q above horizontal from a point 0.9 m up. It lands 5 seconds later, 40 m away horizontally. Find the initial speed. BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 4 A sign is in the shape of a lamina. Find the distance of the centre of mass from AD. A E D 90 cm 40 cm A C 120 cm BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 5 Jane has a four sided dice numbered from 1 to 4. She rolls it twice. Find the probability that the sum of her scores is 7. BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 6 A car of mass 1000kg is moving up an incline of q, where sin q = 1/15. The resistance is R. The engine power is 15 kW, and the speed is 20 ms-1. Find R. BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 7 Find the kinetic energy gained by a 70 kg skier descending 100 m along a 10° downward slope, where m = 0.1 (ignore air resistance). BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 8 A ladder mass 20 kg rests against a smooth wall. The coefficient of friction at the base is ¾. 10 kg is attached at A, and the ladder is about to slip. Find the angle between the ladder and the ground. BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 9 A car travels at 25 m/s. The engine produces a power of 30 kW. Air resistance is 500 N. The coefficient of friction is 0.35. Find the mass of the car. BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 10 Find the distance of the centre of mass from AD C (6m) D (2m) 2a 3a Each rod has mass m BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 11 Find the distance of the centre of mass of the lamina from the centre O… to 5 s.f. 5 cm O BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 12 A 2 kg beam is AB supported horizontally by a free hinge and a rope at C, inclined at 30°. AC = 0.14 m. The tension in the rope is 63 N. Find AB. A C B BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 13 At time t, the velocity of P is given by 𝑣=8𝑡− 3 2 𝑡 2 At time t = 0, s = 0. Find the displacement after 10 s of motion. BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 14 A particle moves with acceleration (3t + 5) ms-2. When t = 0 velocity is 2 ms-1. Later, when t = T the velocity is 6 ms-1. Find T. BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 15 A particle starts from rest and moves with constant acceleration. It travels 1 m in 1 s. How long will it take to travel the next 1 m? BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 16 A toy car goes down a smooth 2 m ramp from rest. It reaches the bottom with velocity 4.07 ms-1. Find the angle of the ramp. BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 17 A hippo is launched from ground level, and lands 3 seconds later 10 m away. Modelling the hippo as a particle, find the angle of projection above horizontal. BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 18 Two particles are connected by a smooth pulley. A (3 kg) is on a smooth 30° slope, B (5 kg) hangs freely, 2 m above the ground. They are released from rest. Find the speed of B when it hits the floor. BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 19 Two particles P and Q collide. The direction of P is reversed. Find the range of possible values for the coefficient of restitution. P 3 kg Q 5 kg 2 ms-1 1 ms-1 BACK TO THE BLOCKBUSTER GRID

BACK TO THE BLOCKBUSTER GRID 20 A 0.5 kg particle is acted on by a force F = (3t2 – 1)i + 2tj. At time t = 2, the velocity is v = (2i + 5j) ms-1. Find the velocity when t = 3. BACK TO THE BLOCKBUSTER GRID