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During a snowball fight , your opponent distracts you by throwing a snowball at you in a high arc. she thriws snowballs with a speed of 24.5 m/s and the first is thrown at 70.0 degrees. As you are watching the first snowball, she throws a second at a lower angle. If both snowballs cover the same horizontal distance, at what angle should the second be thrown?

Respuesta :

Answer:

Explanation:

Given

launch velocity [tex]u=24.5\ m/s[/tex]

first ball launch angle [tex]\theta _1=70^{\circ}[/tex]

Suppose another ball is thrown at an angle of [tex]\theta _2[/tex]

Both ball have same range

Range of Projectile [tex]R=\frac{u^2\sin 2\theta }{g}[/tex]

[tex]R_1=\frac{u^2\sin 2\theta _1}{g}[/tex]

For second ball

[tex]R_2=\frac{u^2\sin 2\theta _2}{g}[/tex]

[tex]R_1=R_2[/tex]

[tex]\frac{u^2\sin 2\theta _1}{g}=\frac{u^2\sin 2\theta _2}{g}[/tex]

[tex]\sin 2\theta _1=\sin 2theta _2[/tex]

Either [tex]\theta _1=\theta _2[/tex] or

[tex]2\theta _1=180-2\theta _2[/tex]

I.e. [tex]\theta _2=90-\theta _1[/tex]

[tex]\theta _2=90-70=20^{\circ}[/tex]

so another ball must be thrown at [tex]20^{\circ}[/tex]