If he throws the ball (with mass 0.07 kg) with a speed of 28 m/s and there is no air resistance, how high does the ball go?

Since the problem did not state any angle of inclination, I assume that the motion was an object thrown up. There are already equation for motions of this kind that are all based from Newton's Laws of Motion. In this case, the maximum height reached by an object, denotes as Hmax, is

Hmax = v₀²/2g, where g is the acceleration due to gravity which is equal to 9.81 m/s and v₀ is the initial velocity of the ball. Substituting the values,

Hmax = (28m/s)²/2(9.81m/s)
Hmax = 39.96 m

Therefore, the ball thrown up could reach as high up to 39.96 meters.

    m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| =  √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| =  √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| =  14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s

Dformation of a precipitate