2D vectors Components:

$\overline{)\begin{array}{rcl}{\mathit{A}}_{\mathit{x}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{A}}\mathbf{\right|}\mathbf{}\mathbf{cos}\mathbf{}\mathit{\theta}\\ {\mathit{A}}_{\mathit{y}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{A}}\mathbf{\right|}\mathbf{}\mathbf{sin}\mathbf{}\mathit{\theta}\end{array}}$

Range:

$\overline{){\mathbf{R}}{\mathbf{=}}\frac{{{\mathbf{v}}_{\mathbf{0}}}^{\mathbf{2}}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{2}\mathbf{\theta}}{\mathbf{g}}}$

**Part A**

Time taken to travel to maximum height, t_{max} is found by:

First, consider the kinematic equation v_{f} = v_{0} + at

At maximum height, v_{fy} = 0

During a baseball game, a baseball is struck at ground level by a batter. The ball leaves the baseball bat with an initial velocity v_{0} = 25 m/s at an angle θ = 15° above horizontal. Let the origin of the Cartesian coordinate system be the ball's position the instant it leaves the bat. Air resistance may be ignored throughout this problem.

Part A. Create an expression in terms of v_{0}, θ, and g for the time t_{max} it takes the ball to travel to its maximum vertical height.

Part B. Calculate the horizonal distance x_{max} in meters the ball has traveled when it returns to ground level.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Projectile Motion concept. You can view video lessons to learn Projectile Motion. Or if you need more Projectile Motion practice, you can also practice Projectile Motion practice problems.