Question

A stone is thrown horizontally from the edge of a cliff with an initial speed vo = 8 m/s. What are the x and y components of its velocity after 1 s of flight? Neglect the effect of air resistance, and use g = 10 m/s?.

Answer 1

Since the only force acting on the stone is its weight the stone only accelerates in the y-direction; this means the following:

• Horizontally we have a uniform rectilinear motion in this direction.

,

• Vertically we have a uniform acceleration motion.

From the previous discussion we readily conclude that after 1 second the horizontal component of the velocity will be 8 m/s.

Now, to determine the y component of the velocity we can use the equation:

`a=(v_f-v_0)/(t)`

in the vertical direction we know that:

The acceleration is -10 m/s^2

The initial velocity is zero.

The time is 1 s.

Plugging these on the equation above and solving for the velocity we have:

`\begin{gathered} (v_f-0)/(1)=-10 \\ v_f=-10 \end{gathered}`

Therefore, after one second we have:

`\begin{gathered} v_x=8\text{ m/s} \\ v_y=-10\text{ m/s} \end{gathered}`