Question

A tennis ball is kicked horizontally off the edge of a 25 m high building and lands a distance of 27 m from the edge of the building. What was the final horizontal velocity of the tennis ball, in m/s? Ignore air resistance.

Answer 1

Given:

Height = 25 m

Distance from the edge to where it lands = 27 m.

Let's find the final horizontal velocity of the tennis ball.

To find the final horizontal velocity of a projectile motion, apply the formula:

$v_{fx}=v_ix$

The initial horizontal velocity and the final horizontal velocity are the same since there is no force acting on the object.

Now, to find the horizontal velocity, let's first make a free sketch of this situation:

Let's find the time of flight:

$t=\sqrt{\frac{2h}{g}}$

Where:

h = 25 m

g is acceleration due to gravity = 9.8 m/s²

Thus, we have:

$\begin{gathered} t=\sqrt{\frac{2*25}{9.8}} \\ \\ t=2.26\text{ s} \end{gathered}$

The time of flight if the projectile is 2.26 seconds.

Now, to find the final horizontal velocity, we have:

$\begin{gathered} V=\frac{x}{t} \\ \end{gathered}$

Where:

x is the horizontal distance = 27 m

Thus, we have:

$\begin{gathered} V=\frac{27}{2.26} \\ \\ V=11.96\text{ m/s} \end{gathered}$

Therefore, the final horizontal velocity is 11.96 m/s.

ANSWER:

11.96 m/s