Two balls are thrown from the same height as shown. the red ball is thrown with velocity v⃗ v→ in the vertical direction. the blue ball is thrown with velocity 2v⃗ 2v→ at an angle of 30o with respect to the horizontal. which ball will go higher?

both balls will go the same height.

Explanation:

The height is related only with the vertical velocity.

With the angle of 30° respect the horizontal you can calculate the vertical velocity from the sine ratio:

sin(30°) = vertical speed / speed = > vertical speed = speed * sin(30°)

=> vertical speed = speed * 0.5 = (2v) * 0.5 = v.

That means that both balls are thrown with the same vertical velocity, therefore both balls will go the same height.