HW7 #7

Student question:
I tried to do #7, but it doesn't seem to work. I have the following values given:
A projectile of mass 5 kg is fired with an initial speed of 198 m/s at an angle of 25◦ with the horizontal. At the top of its trajectory, the projectile explodes into two fragments of masses 3.2 kg and 1.8 kg . The 1.8 kg fragment lands on the ground directly below the point of explosion 2.8 s after the explosion.

The acceleration due to gravity is 9.81 m/s2 .
Find the magnitude of the velocity of the 3.2 kg fragment immediatedly after the explosion.

I know that the 1.8 kg has no horizontal velocity because it falls straight down, so I found the horizontal velocity of the 3.2 kg fragment by doing (5 kg)(198cos25 m/s)/(3.2 kg). I tried to find the vertical velocity by finding the initial vertical velocity of the 1.8 kg. I used X=V0t+1/2at^2 and used conservation of energy in the vertical direction to find the height, or X. I then put this velocity into conservation of momentum in the vertical direction and found the vertical velocity for the 3.2 kg fragment. Finally, I used the pythagorean triangle to find the resulting velocity. I've done this five times and it hasn't worked. Am I doing something wrong or missing some important step? If you could reply as soon as possible, I'd greatly appreciate it. Thanks!

Dr. Winters' response:
Very nice start. This is a fairly complex problem, where you need to look at kinematics and momentum. I like the way you found the horizontal component of the 3.2kg fragment using conservation of momentum in the horizontal direction.

I didn't follow how you found the vertical velocity of the 1.8kg fragment. It sounds as though you first found the vertical velocity and then found the height. I think that's backwards. You can find the height using kinematics (the explosion takes place at the top of the trajectory). Knowing the height and the time to fall, you can find the initial vertical velocity of the 1.8kg fragment.

After that, use conservation of momentum in the vertical direction, as you described, to find the vertical component of velocity of the 3.2kg fragment.

It sounds as though you are doing everything right except attacking the middle calculation backwards. Hope that helps. Good luck.