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A daredevil is shot out of a cannon at 51.7 ◦ to the horizontal with an initial speed of 31.9 m/s. A net is positioned a horizontal distance of 39.1 m from the cannon. At what height above the cannon should the net be placed in order to catch the daredevil? The acceleration of gravity is 9.8 m/s 2 . Answer in units of m.

Respuesta :

Answer:30.34 m

Explanation:

Given

launch angle[tex]=51.7^{\circ}[/tex]

Initial velocity u=31.9 m/s

Position of net = 39.1 m

We know equation of trajectory of a projectile is

[tex]y=x\tan \theta -\frac{gx^2}{2u^2(\cos \theta )^2}[/tex]

[tex]y=39.1\times \tan 51.7-\frac{9.8\times 39.1^2}{2\times 31.9^2\times (cos51.7)^2}[/tex]

[tex]y=49.509-\frac{9.8\times 1.502}{2\times 0.384}[/tex]

[tex]y=49.509-\frac{14.719}{0.768}[/tex]

[tex]y=49.509-19.165=30.343 m[/tex]

Therefore Net should be placed 30.34 m above ground

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