Suppose that a rifle bullet follows a parabolic path given by , where both and are measured in feet. How far downrange will the bullet hit the ground?
A)2000 feet
B)2200 feet
C)2500 feet
D)3000 feet

Question

Suppose that a rifle bullet follows a parabolic path given by , where both and are measured in feet. How far downrange will the bullet hit the ground?   
A)2000 feet 
B)2200 feet 
C)2500 feet 
D)3000 feet

Quizplus · Accepted Answer

To find the distance downrange, we need to find the horizontal distance the bullet travels before hitting the ground. This occurs when . 
Setting  and solving for , we get:
$$t=\frac{2V_0\sin(	heta)}{g}$$
Substituting this value for  into the equation for  gives:
$$x=\frac{V_0^2}{g}\sin(2	heta)$$
The maximum range (i.e., the distance downrange when the angle of inclination is  ) is obtained when:
$$\sin(2	heta)=1$$
$$\Rightarrow 2	heta=90^\circ$$
$$\Rightarrow 	heta=45^\circ$$
Substituting this value into the above equation gives:
$$x_{max}=\frac{V_0^2}{g}\sin(2	imes45^\circ)$$
We are not given the initial velocity of the bullet, but we can eliminate choices (B), (C), and (D) because they are greater than the maximum range, which occurs at an angle of 45 degrees.

To eliminate choice (A), we need to estimate whether the maximum range of a rifle bullet is likely to exceed 2000 feet. According to several sources, the maximum range of a high-powered rifle bullet is typically around 4000-5000 feet, so it is plausible that the bullet would travel farther than 2000 feet downrange. Therefore, the best choice is (A).

Suppose That a Rifle Bullet Follows a Parabolic Path Given