A projectile is launched from ground level at an angle of $\theta$ with the horizontal. The initial velocity is $v _ { 0 }$ feet per second and the path of the projectile is modeled by the parametric equations $x = \left( v _ { 0 } \cos \theta \right) t \text { and } y = \left( v _ { 0 } \sin \theta \right) t - 16 t ^ { 2 } \text {. }$
Use a graphing utility to graph the paths of a projectile launched from ground level with the values given for $\theta$ and $v _ { 0 }$. Use the graph to approximate the maximum height and range of the projectile to the nearest foot.
$\theta = 55 ^ { \circ } , \quad v _ { 0 } = 56 \text { feet per second }$
A) maximum height $\approx 49$ feet range $\approx 4$ feet
B) maximum height $\approx 4$ feet range $\approx 49$ feet
C) maximum height $\approx 33$ feet range $\approx 92$ feet
D) maximum height $\approx 92$ feet range $\approx 33$ feet
E) maximum height $\approx 43$ feet $\quad$ range $\approx 8$ feet

Question

Quizplus · Accepted Answer

The maximum height and range of a projectile can be calculated using the given parametric equations and the initial conditions. For a projectile launched at an angle $\theta$ with an initial velocity $v_0$, the maximum height is achieved when the vertical velocity component is zero, and the range is the horizontal distance covered when the projectile hits the ground. Given $\theta = 55^\circ$ and $v_0 = 56$ feet per second, the correct approximation for maximum height and range is $\approx 33$ feet and $\approx 92$ feet, respectively, when calculated or graphed using the provided equations.

A Projectile Is Launched from Ground Level at an Angle θ\thetaθ

A Projectile Is Launched from Ground Level at an Angle $\theta$