Question

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°

Answer 1

`a)\text{ }57\degree`

Step-by-step 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:

`R=(u^2\sin2\theta)/(g)`

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°)):

`\sin(2*33)=\sin66=0.9135`

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

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

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

The answer is option a.