# A projectile is shot at a velocity of #37 m/s# and an angle of #pi/12 #. What is the projectile's maximum height?

##### 2 Answers

The maximum height is

#### Explanation:

The maximum height is obtained from the formula

The vertical component of the velocity is

At the maximum height,

So,

The maximum height of the projectile is

#### Explanation:

To find the projectile's maximum altitude, or maximum height, we can make use of kinematic equations. Namely,

Because the projectile is launched at an angle, it is necessary to break up the given initial velocity into horizontal and vertical components. This can be done using basic trigonometry.

We take the initial velocity to be

*Note:* Diagram not to scale.

For this problem, we require only the vertical velocity component.

As we know that

We will assume this to be the *initial* vertical velocity of the projectile, while the *final* vertical velocity of the projectile will be

Because this object is in free-fall, its vertical acceleration is equal to

Rearrange to solve for

The maximum altitude of the projectile is