Two boys are sliding toward each other on a frictionless, ice-covered parking lot. Jacob, mass 45 kg, is gliding to the right at 7.67 m/s, and Ethan, mass 31.0 kg, is gliding to the left at 10.8 m/s along the same line. When they meet, they grab each other and hang on.

(a) What is their velocity immediately there after?

magnitude

direction

(b) What fraction of their original kinetic energy is still mechanical energy after their collision?

(c) That was so much fun that the boys repeat the collision with the same original velocities, this time moving along parallel lines 1.04 m apart. At closest approach, they lock arms and start rotating about their common center of mass. Model the boys as particles and their arms as a cord that does not stretch. Find the velocity of their center of mass.

magnitude

direction

(d) Find their angular speed.

Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. rad/s

(e) What fraction of their original kinetic energy is still mechanical energy after they link arms?
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.