Answer Happy

m S5. Two small uniform smooth spheres have masses m and 3m, and speeds 7u and 2u in opposite directions, respectively. They collide directly, and the lighter mass is brought to rest by the collision. Find the coefficient of restitution. S6. A monetary investment grows so that if P(t) is the balance in an account at time dP t (measured in years), then 0.05P(). With an initial investment of € 100, dt how much money is in the account after one year (to the nearest cent)? S7. Find the position vector of the centre of mass of the particles of masses m, 2m, 4m and 3m at the points with positions vectors r = i+k, r, = 3i+ 4k, r3 = -5i +2j - k and r^=i+2j + 8k, respectively. S8. A disc of mass m and radius R rolls down a slope of incline 60°. The slope is rough enough to prevent slipping. The disc travels from rest a distance 120 m down the slope. The gravitational constant is g = 10 ms 2. Show that the final linear velocity of the disc is 37.2 ms-1. (Assume without proof that the reaction force does no work.