A 10 g bullet is fired horizontally from a 2 kg rifle hanging from a string...?

10/1000 = 0.01 kg

0.01 x 1000 = 10 kg-m/s

10 kg-m/s = 2v

10/2 = v = 5 m/s

before firing momentum was zero

after firing momentum should remain zero since no external force acts

10 g is .01 kg

final momentum

.01 * 1000 + 2 * v = 0

10 + 2v = 0

v = -5 m/s

so the velocity of the rifle is 5m/s opposute to the direction of the bullet

utilising conservation of momentum for an inelastic collision, m0*v0=(m(pendulum)+m0)*v(new), therefore the cost of the hot device might want to be m0*v0/(m(pendulum)+m0)=v(new). Now we use conservation of potential to work out how the kinetic potential alterations into gravitational potential potential. 0.5*m(device)*v(new)^2=m(device)*g*heigh... the position mass cancel and the properly would properly be defined as properly=v(new)^2/(2*g). properly is the vertical displacement. Horizontal displacement would properly be got here upon utilising trigonometry. the bottom of the triangle, horizontal displacement, is what needs to be got here upon. utilising Pythagoras' theorem the hypotenuse is the dimensions of the string, l, and one in each and every of the different aspects is =l-properly. to that end all you would possibly want to do is horizontal displacement=sqrt(l^2-(l-properly)^2)