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In the absence of air resistance, a projectile launched at an angle of 33° above the horizontal will have the same range as a projectile launched at which of the following angles?a.)57°b.)38° c.)45°

Respuesta :

ANSWER

[tex]a)\text{ }57\degree[/tex]

EXPLANATION

We want to find the angle at which the range for the projectiles will be the same.

The range for a projectile is given by:

[tex]R=\frac{u^2\sin2\theta}{g}[/tex]

where u = initial velocity

θ = angle of the projectile

g = acceleration due to gravity

For a projectile to have the same range as one with an angle of 33° (given that other values are constant), the value of sin(2θ) must be equal for both projectiles.

Let us find the value of sin(2(33°)):

[tex]\sin(2*33)=\sin66=0.9135[/tex]

Let us find the same for the angles in the options:

[tex]\begin{gathered} \sin(2*57)=\sin114=0.9135 \\ \\ \sin(2*38)=\sin76=0.9703 \\ \\ \sin(2*45)=\sin90=1 \end{gathered}[/tex]

As we can see, the angle that will result in the same range as 33° is 57°.

The answer is option a.

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