# A tennis player hits a ball vertically with a speed of 10 m/s. How high does it go?

##### 2 Answers

The ball reaches a height of 5.1 m.

#### Explanation:

The formula we are going to use is:

=> where

Acceleration is

#(V_"f"^2) = (V_"i"^2) + 2aDeltad#

#0 = 10^2 + 2(-9.8)Deltad#

#0 = 100 - 19.6Deltad#

#-100 = -19.6Deltad#

#5.1 = Deltad#

The change in displacement is 5.1 m. Assuming the player is on the ground (0 m), that means the ball reaches a height of 5.1 m.

Hope this helps :)

The maximum altitude of the ball is

#### Explanation:

There are at least two ways to solve this, one being with kinematics and the other with energy conservation. These are just the first two that come to mind. I'll give an explanation of both methods.

**Kinematics:**

This problem exemplifies projectile motion. What is important to recognize here is that at its maximum altitude, the velocity of the ball will be

Solving for

We know that

**Energy Conservation:**

Where

As the ball is moving initially, for our intents and purposes it possesses only kinetic energy, the energy associated with motion (we can assign and initial height of

This tells us that all of the energy the ball possesses initially in the form of kinetic energy is stored as potential energy when the ball is at its maximum altitude, which will then be converted back into kinetic energy when the ball is falling back to Earth.

Kinetic energy is given by

We can see that mass cancels, yielding:

Solving for

Using

Hope that helps!