Vector components:

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

We're also going to use the kinematic equation:

$\overline{){\mathbf{\u2206}}{\mathbf{y}}{\mathbf{=}}{{\mathbf{v}}}_{\mathbf{0}\mathbf{y}}{\mathbf{t}}{\mathbf{-}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{g}}{{\mathbf{t}}}^{{\mathbf{2}}}}$

The components of the velocity:

v_{0x} = v_{0}cosθ = (30.6)cos(36.3°) = 24.66 m/s

v_{0y} = v_{0}sinθ = (30.6)sin(36.3°) = 18.12 m/s

**A.**

From the kinematic equation Δy = v_{0y}t - (1/2)gt^{2}, we can get the times as:

A major leaguer hits a baseball so that it leaves the bat at a speed of 30.6 m/s and at an angle of 36.3° above the horizontal. You can ignore air resistance.

You may want to review (Pages 75 - 82).

For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Height and range of a projectile i: a batted baseball.

A. At what *two* times is the baseball at a height of 10.9 m above the point at which it left the bat?

B. Calculate the horizontal component of the baseballs velocity at an earlier time calculated in part (a).

C. Calculate the vertical component of the baseballs velocity at an earlier time calculated in part (a).

D. Calculate the horizontal component of the baseballs velocity at a later time calculated in part (a).

E. Calculate the vertical component of the baseballs velocity at a later time calculated in part (a).

F. What is the magnitude of the baseballs velocity when it returns to the level at which it left the bat?

G. What is the direction of the baseballs velocity when it returns to the level at which it left the bat?

Frequently Asked Questions

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

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Based on our data, we think this problem is relevant for Professor Yildirim's class at ASU.