What is the resulting speed of two objects (one launched at a curved path and one free falling) upon reaching the ground?

Question

Upon reaching its maximum height, a 546-g projectile launched from the ground with an initial velocity of 15.0 m/s, 30.0° above the horizontal collides with a vertical free falling object of mass 245 g and the two stick together after the collision. Suppose that at the time of collision, the second object is momentarily at rest, what is the resulting speed of the two objects upon reaching the ground?

Answer 1

At the moment of collision the vertical speeds of both particles are zero.

After they stick together they fall vertically under free fall, with their speed on the ground vertically being 15 sin 30 (original vertical speed of first particle) = 7.5 m/s

Horizontally we need to consider momentum

Momentum of first object at moment of collision = mv = 0.546 x 15 cos 30

Momentum of second object = 0

Total momentum (constant) = 0.546 x 15 cos 30

After collision total mass = 791 g = 0.791 kg

So if v is new horizontal speed 0.791 v = 0.546 x 15 cos 30, giving v = 8.967 m/s

So speed on the ground = √ (7.5² + 8.967²) = 11.69 m/s