Please answer both parts for full rating PART A Suppose m is a certain mass and

Question

Please answer both parts for full rating

PART A

Suppose m is a certain mass and v is a certain speed v>0. A mass m_1 = 5m moving to the right with a velocity v_1 = +8v collides head-on with a second mass m_2 = 4m moving to the left with a velocity v_2 = -3v. The two masses stick together to form a single mass moving with velocity v_f = n v, where n is a number (no units). What is n?

PART B

A 26.0-kg shell is fired from a gun with a muzzle velocity 85.0 m/s at 26.0o above the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass. One fragment, whose speed immediately after the explosion is zero, falls vertically. What is the horizontal speed of the other fragment?

Explanation / Answer

1.

By Conservation of momentum

m1V1 + m2V2 =(m1+m2)Vf

5m*8v +4m*(-3v) =(5m+4m)*(nv)

n=28/9 =3.1111

2.

By COnservation of momentum in x-direction

mVx =m1V1x +m2V2x

26*(85cos26) = (26/2)*0 +(26/2)*V2x

V2x=152.8 m/s

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