I am having trouble determining the direction angle for both parts b and c. Can someone point me in the right direction. I did figure out the height for both but am lost as to how to go from here. Thanks for your help.

Question Details:
In Figure 9-44, two particles are launched from the origin of the coordinate system at time t = 0. Particle 1 of mass m1 = 5.00 g is shot directly along an x axis (on a frictionless floor), where it moves with a constant speed of 17.0 m/s. Particle 2 of mass m2 = 3.00 g is shot with a velocity of magnitude 34.0 m/s, at an upward angle such that it always stays directly above particle 1 during its flight.

(a.) What is the maximum height Hmax reached by the center of mass of the two-particle system? ____m
(b.) What is the magnitude and direction of the velocity of the center of mass when the center of mass reaches this height? ____ m/s and _____° (counterclockwise from the positive x axis)
(c.) What is the magnitude and direction of the acceleration of the center of mass when the center of mass reaches this height? ____ m/s2 ____° (counterclockwise from the positive x axis)

because only the velocity of the particle fired at an angle is changing (and that only in the vertical direction), and since at its maximum height its instantaneous vertical velocity is zero, and since the velocities of the two particles in the x-axis (horizontal as I am terming it) direction are equal the velocity of the center of mass at that instant would be equal (in magnitude and direction) to that of the particle travelling horizontally

the acceleration of the center of mass when particle two is at its maximum height has a magnitude that is equal to the acceleration acting on particle 2 multiplied by the ratio of the mass of particle 2 to the sum of the masses of particles 1 and 2, the direction of the acceleration is is along the y-axis (because this is the only direction of acceleration that allows particle 2 to always be above particle 1)

I hope that helps.

Thank you that helps a lot!!!! Thanks so much. Would the direction of the acceleration be negative or positive along the y-axis (I'm obviously very confused about this!). I tried using 90 degrees for the direction of the acceleration but that was wrong.

negative (as long as particle 2 is being fired with an angle of less than 180), so 270 should be correct

Thank you - yes, I just tried that and it was right but I appreciate you getting back to me so quickly. Your responses were really helpful and I think I will be able to answer another question like this now. Thanks again - you don't know how much time I spent trying to figure this out. I struggle with physics!