Question

1. the path of a projectile is a linear curve / round curve / parabolic curve 6. without air resistance, maximum range of a projectile is obtained with an angle of_______. 7. the same range can be obtained with angles of _____ and _______.

Explanation:

Step1: Recall range formula

The range formula of a projectile is $R=\frac{v_0^2\sin2\theta}{g}$, where $v_0$ is the initial velocity, $\theta$ is the angle of projection and $g$ is the acceleration due to gravity.

Step2: Find maximum - range angle

We know that the function $y = \sin2\theta$ has a maximum value of 1. Since $\sin2\theta=1$ when $2\theta = 90^{\circ}$, then $\theta = 45^{\circ}$.

Step3: Find angles for same range

We know that $\sin2\theta=\sin(180 - 2\theta)$. If the angles of projection are $\theta_1$ and $\theta_2$ such that $2\theta_1=180 - 2\theta_2$, or $\theta_2 = 90^{\circ}-\theta_1$. So the same range can be obtained with angles $\theta$ and $90^{\circ}-\theta$.

Answer:

1. $45^{\circ}$
2. $\theta$, $90^{\circ}-\theta$