Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

A projectile is launched at ground level with an initial speed of $50.0 m / s$ at an angle of $30 . 0^{o}$ above the horizontal. It strikes a target above the ground $3.00$ seconds later. What are the x and y distances from where the projectile was launched to where it lands?

The projectile strikes a target at a distance of $130$ meters horizontally and $30.9$ meters vertically from the launching point.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Determine projectile Motion

The projectile is a missile that moves freely under the influence of gravity and air resistance after being propelled by an external source.

A projectile is an object that is traveling in both the horizontal and vertical directions at the same time. Projectile motion is always in the form of a parabola.

Given Data:

Initial speed = 50.0 m/s
Angle above the horizontal = $30^{\circ}$
Time = 3 s.

Step 2: Determine components of initial velocity

Since we do not know the exact location of the projectile after $3$ s.

Components of the initial velocity can be calculated as:

$\begin{array}{rcl} (V_{o x}) & = & (50) \cos 30^{°} \\ = & 43.3013 m / s \\ (V_{o y}) & = & (50) \sin 30^{°} \\ = & 25 m / s \end{array}$

Step 3: To solve the values of x and y:

Horizontal displacement X can be calculated as:

$X = v_{o x} t$

Substituting values in the above expression, we get,

$\begin{array}{rcl} X & = & (43.3013) \times (3) \\ X & = & 130 m \end{array}$

Vertical displacement Y can be calculated as:

$Y = v_{o y} t + \frac{1}{2} a t^{2}$

Substituting values in the above expression, we get,

$\begin{array}{rcl} Y & = & (25 m/s) \times (3 s) + \frac{1}{2} \times (- 9.8) \times {(3 s)}^{2} \\ Y & = & 30.9 m \end{array}$

Therefore, the projectile strikes a target at a distancerole="math" localid="1668679240901" $130 m$ horizontally and $30.9 m$ vertically from the launching point.

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College Physics (Urone)

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Short Answer

A projectile is launched at ground level with an initial speed of $50.0 m / s$ at an angle of $30 . 0^{o}$ above the horizontal. It strikes a target above the ground $3.00$ seconds later. What are the x and y distances from where the projectile was launched to where it lands?

Step by Step Solution

Step 1: Determine projectile Motion

Step 2: Determine components of initial velocity

Step 3: To solve the values of x and y:

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College Physics (Urone)

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Short Answer

A projectile is launched at ground level with an initial speed of 50.0m/s at an angle of30.0o above the horizontal. It strikes a target above the ground 3.00seconds later. What are the x and y distances from where the projectile was launched to where it lands?

Step by Step Solution

Step 1: Determine projectile Motion

Step 2: Determine components of initial velocity

Step 3: To solve the values of x and y:

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A projectile is launched at ground level with an initial speed of $50.0 m / s$ at an angle of $30 . 0^{o}$ above the horizontal. It strikes a target above the ground $3.00$ seconds later. What are the x and y distances from where the projectile was launched to where it lands?