Question

What is the velocity of an object if we throw it at a certain angle with double its initial velocity?

Answer 1

If we assume the initial velocity of the object to be $v_0$, throwing it at a certain angle with double its initial velocity means the new initial velocity will be $2v_0$.

To determine the final velocity of the object, we need to know the specifics of the object's motion, such as the angle at which it was thrown, the initial speed, and any other forces acting on it (like air resistance).

Assuming we are working in a vacuum with no air resistance, and neglecting any other forces, we can use the basic principles of projectile motion to calculate the final velocity.

In projectile motion, the horizontal and vertical motions are independent of each other. The horizontal velocity ($v_x$) remains constant throughout the motion, while the vertical velocity ($v_y$) changes due to the influence of gravity.

Let's assume the angle at which the object was thrown is $\theta$. We can break down the initial velocity into its horizontal and vertical components:

$v_{0x}=v_0\cos (\theta )$ (horizontal component) $v_{0y}=v_0\sin (\theta )$ (vertical component)

When the object reaches its highest point, the vertical velocity becomes zero ($v_{y_f}$