Answer:
a) The fragment speeds of 0.3 kg is 33.3 m / s on the y axis
                                          0.7 kg is 109.4 ms on the x axis
b)  Y = 109.3 m
Explanation:
This is a moment and projectile launch exercise.
a) Let's start by finding the initial velocity of the projectile
        sin 40 = voy / v₀
         = v₀ sin 40
 = v₀ sin 40
         = 50.0 sin40
 = 50.0 sin40
         = 32.14 m / s
 = 32.14 m / s
        cos 40 = v₀ₓ / V₀
        v₀ₓ = v₀ cos 40
        v₀ₓ = 50.0 cos 40
        v₀ₓ = 38.3 m / s
Let us define the system as the projectile formed t all fragments, for this system the moment is conserved in each axis
Let's write the amounts
Initial mass of the projectile M = 2.0 kg
Fragment mass 1 m₁ = 1.0 kg and its velocity is vₓ = 0 and  = -10.0 m / s
 = -10.0 m / s
Fragment mass 2 m₂ = 0.7 kg moves in the x direction
Fragment mass 3 m₃ = 0.3 kg moves up (y axis)
Moment before the break
X axis
      p₀ₓ = m v₀ₓ
Y Axis y
      = 0
 = 0
After the break
X axis
     = m₂ v₂
 = m₂ v₂
Axis y
       = m₁ v₁ + m₃ v₃
 = m₁ v₁ + m₃ v₃
Let's write the conservation of the moment and calculate
Y Axis  
      0 = m₁ v₁ + m₃ v₃
Let's clear the speed of fragment 3
      v₃ = - m₁ v₁ / m₃
      v₃ = - (-10) 1 / 0.3
      v₃ = 33.3 m / s
X axis
      M v₀ₓ = m₂ v₂
      v₂ = v₀ₓ M / m₂
      v₂ = 38.3  2 / 0.7
      v₂ = 109.4 m / s
The fragment speeds of 0.3 kg is 33.3 m / s on the y axis
                                          0.7 kg is 109.4 ms on the x axis
b) The speed of the fragment is 33.3 m / s and has a starting height of where the fragmentation occurred, let's calculate with kinematics
         ² =
² =  ² - 2 gy
² - 2 gy
        0 =   ²-2gy
²-2gy
        y =   ² / 2g
² / 2g
        y = 32.14² / 2 9.8
        y = 52.7 m
This is the height where the break occurs, which is the initial height for body movement of 0.3 kg
        ² =
² =   ² - 2 g y₂
² - 2 g y₂
       0 =   ² - 2 g y₂
² - 2 g y₂
      y₂ =   ² / 2g
² / 2g
      y₂ = 33.3²/2 9.8
      y₂ = 56.58 m
Total body height is
       Y = y + y₂
       Y = 52.7 + 56.58
      Y = 109.3 m