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A small pumpkin is launched from a very versatile catapult at a variety of speeds and angles. The angles are measured relative to the horizontal. Rank each of the following trials by the maximum height reached by the pumpkin. (1=highest) Consider air resistance to be negligible.
1 2 3 4 Speed: 30.7m/s, Angle: 35.7°
1 2 3 4 Speed: 47.9m/s, Angle: 33.2°
1 2 3 4 Speed: 21.8m/s, Angle: 67.7°
1 2 3 4 Speed: 7.7m/s, Angle: 62.1°

Respuesta :

Answer:

Explanation:

Maximum height of a projectile

[tex]H_{max}=\frac{u^2\sin ^2\theta }{2g}[/tex]

(1)[tex]u=30.7\ m/s[/tex]

[tex]\theta =35.7^{\circ}[/tex]

[tex]H_1=\frac{30.7^2\times \sin ^2(35.7)}{2\times 9.8}[/tex]

[tex]H_1=16.37\ m[/tex]

(2)[tex]u=47.9\ m/s[/tex]

[tex]\theta =33.2^{\circ}[/tex]

[tex]H_2=\frac{47.9^2\times \sin ^2(33.2)}{2\times 9.8}[/tex]

[tex]H_2=35.09\ m[/tex]

(3)[tex]u=21.8\ m/s[/tex]

[tex]\theta =67.7^{\circ}[/tex]

[tex]H_3=\frac{21.8^2\times \sin ^2(67.7)}{2\times 9.8}[/tex]

[tex]H_3=20.75\ m[/tex]

(4)[tex]u=7.7\ m/s[/tex]

[tex]\theta =62.1^{\circ}[/tex]

[tex]H_4=\frac{7.7^2\times \sin ^2(62.1)}{2\times 9.8}[/tex]

[tex]H_4=2.36\ m[/tex]      

Therefore height reached by pumpkin can be arranged as

[tex]H_4<H_1<H_3<H_2[/tex]

 

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