A baseball is hit 3 feet above the ground at 100 feet per second and at an angle of 45 ^{\circ} ...

Question:

A baseball is hit 3 feet above the ground at 100 feet per second and at an angle of 45{eq}^{\circ} {/eq} with respect to the ground.

a. Find the vector-valued function for the path of the baseball.

b. Find the maximum height.

c. Find the range.

d. Find the arc length s of the trajectory.

Projectile Motion:

This scenario described a parabolic motion, which is known as a double motion since it has two components, one horizontal and one vertical. In the same way, the velocity of the ball and the acceleration of the ball has two components.

We can relate these vectors in this way:

Velocity: {eq}v\left(t\right)=r'\left(t\right) {/eq}

Acceleration: {eq}a\left(t\right)=v'\left(t\right) {/eq}

Answer and Explanation:

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Data:

{eq}v_{o}=100\:\frac{ft}{s} \\ \theta=45^{\circ} \\ y_{o}=3\:ft \\ g=32\:\frac{ft}{s^2} {/eq}


Position Vector:

{eq}\mathbf...

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Projectile Motion: Definition and Examples

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Chapter 4 / Lesson 13
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A projectile is any object that is given an initial velocity and then follows a path determined entirely by gravity. In this lesson, we will introduce projectile motion and touch on a few key facts to keep in mind when working through these problems.


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