Chapter 6.6, Problem 92E

(a)

To determine

To graph: The paths of a projectile launched from the ground level at $\theta =15°$, $v_0=50\text{ feet per second}$, and approximate the maximum height and range of the projectile with the help of the graph, the initial velocity and path of projectile have the parametric equations as $x=\left(v_0\cos \theta \right)t$ and $y=h+\left(v_0\sin \theta \right)t-16t^2$, where $h$ represents the height above the ground.

(b)

To determine

To graph: The paths of a projectile launched from ground level at $\theta =15°$, $v_0=120\text{ feet per second}$, and approximate the maximum height and the range of the projectile with the help of the graph, the initial velocity and path of projectile have the parametric equations as $x=\left(v_0\cos \theta \right)t$ and $y=h+\left(v_0\sin \theta \right)t-16t^2$, where $h$ represents the height above the ground.

(c)

To determine

To graph: The paths of a projectile launched from ground level at $\theta =10°$, $v_0=50\text{ feet per second}$, and approximate the maximum height and the range with the help of graph , the initial velocity and path of projectile have the parametric equations as $x=\left(v_0\cos \theta \right)t$ and $y=h+\left(v_0\sin \theta \right)t-16t^2$. But here the projectile is launched from the ground so that the parametric equations would be $x=\left(v_0\cos \theta \right)t$ and $y=\left(v_0\sin \theta \right)t-16t^2$, where $h$ represents the height above the ground.

(d)

To determine

To graph: The paths of a projectile launched from the ground level at $\theta =10°$, $v_0=120\text{ feet per second}$, and approximate the maximum height and the range of the projectile with the help of the graph, the initial velocity and path of projectile have the parametric equations as $x=\left(v_0\cos \theta \right)t$ and $y=h+\left(v_0\sin \theta \right)t-16t^2$, where $h$ represents the height above the ground.