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
$x = \left( v _ { 0 } \cos \theta \right) t$ and $y = \left( v _ { 0 } \sin \theta \right) t - 16 t ^ { 2 }$.
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.
$\theta = 55 ^ { \circ } , \quad v _ { 0 } = 56$ 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 range $\approx 8$ feet

Question

Quizplus · Accepted Answer

The maximum height and range of a projectile can be determined from its parametric equations. Given the initial speed $v_0 = 56$ feet per second and launch angle $\theta = 55^\circ$, the maximum height and range can be calculated or approximated using physics formulas or graphing utilities. The correct choice reflects a realistic outcome for such a projectile, where the maximum height is significant but less than the range, given the angle and initial velocity.

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

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