A 5.0 bowling ball is perched on the edge of the roof of a 10-meter high wall. Another bowling ball with a mass of 8.0 kg is rolled down a 10 m long ramp inclined at 30 degrees with the rooftop. It strikes the other bowling ball and the two roll off the rooftop. How far apart do the two balls land?
first calculate the velocity of 8kg ball before the impact using energy conservation
1/2mv^2 = mg(10sin30)
v = root ( 10g) = 10m/sec approximately
next
use momentum conservation horizontal impact of the two balls
initial momentum = 8*10 = 80
final momentum = 5u + 8v
kinetic energy is also conserved in elastic collisions
800 = 5u^2 + 8v^2
solve this to get v = 30/13 for 8kg ball
u = 160/13 for 5 kg ball
now the velocities are horizontal and have no vertical component so they both fall at the same time on the ground since they start with same vertical velocity and have the same vertical acceleration so it makes snese . but how fat apart they land horizontally is our question and we know the horizontal component remains the same since there is no horizontal force
10 = 1/2gt^2
time = root2 assuming g as 10
difference in distance they land horizontally = (160/13 - 30/13) root2 = 10root2 = 14.14 m approx
hope thjis is clear
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