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A small missile is fired with a velocity of \(300 \mathrm{~m} / \mathrm{s}\) at an angle of 30 degrees.

a.) Determine the initial horizontal and vertical velocity.
b.) Determine the time to reach maximum height and the total time of the flight.
c.) Determine the maximum height.
d.) Determine the horizontal range.
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in Mathematics by Platinum (122,212 points) | 20 views
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a.) Determine the initial horizontal and vertical velocity.

\[\cos{30^{\circ}}= \dfrac{\text{adjacent}}{\text{hypotenuse}} = \dfrac{x}{300}\]

\[\implies x = 300 \times \cos{30^{\circ}}\]

\[\therefore x= 259.81m/s\]


b.) Determine the time to reach maximum height and the total time of the flight.

Total Time of Flight \((t)=\frac{2 u \sin \theta}{g}\)

\[t=\dfrac{2\cdot 300 \cdot \sin 30^{\circ}}{10} = 30s\]


c.) Determine the maximum height.

The maximum height of the projectile is given by the formula:
\[
H=\dfrac{v_{0}^{2} \sin ^{2} \theta}{2 g}
\]

Assuming \(g=10m/s^2\)

\[
H=\dfrac{300^{2} \sin ^{2} 30^{\circ}}{2\cdot 10}
\]

\[
H=\dfrac{300^{2} \sin ^{2} 30^{\circ}}{2\cdot 10} = 1125m
\]

 


d.) Determine the horizontal range.

Horizontal Range \((R)=\dfrac{u^{2} \sin 2 \theta}{g}\)

Assuming \(g=10m/s^2\)

 

\[(R)=\dfrac{300^{2} \sin{60^{\circ}}}{10} = 7794.23m\]

 

by Platinum (122,212 points)
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