If a projectile is fired with an initial velocity of $v _ { 0 }$ meters per second at an angle $\alpha$ above the horizontal and air resistance is assumed to be negligible, then its position after $t$ seconds is given by the parametric equations
$x = \left( v _ { 0 } \cos \alpha \right) t , y = \left( v _ { 0 } \sin \alpha \right) t - \frac { 1 } { 2 } g t ^ { 2 }$ where $g$ is the acceleration of gravity $\left( 9.8 \mathrm {~m} / \mathrm { s } ^ { 2 } \right)$. If a gun is fired with $\alpha = 55 ^ { \circ }$ and $v _ { 0 } = 440 \mathrm {~m} / \mathrm { s }$ when will the bullet hit the ground?
A) $t = 244 \mathrm {~s}$
B) $t = 74 \mathrm {~s}$
C) $t = 344 \mathrm {~s}$
D) $t = 124 \mathrm {~s}$
E) $t = 224 \mathrm {~s}$

Question

Quizplus · Accepted Answer

To find when the bullet will hit the ground, we set $y = 0$ and solve for $t$. Substituting $\alpha = 55^\circ$ and $v_0 = 440 \, \text{m/s}$ into the equation for $y$, we get:$$0 = (440 \sin 55^\circ)t - \frac{1}{2} \cdot 9.8 \cdot t^2$$Solving this quadratic equation for $t$ gives the time when the bullet will be at ground level. The correct calculation leads to $t = 74 \, \text{s}$, which matches choice B.

If a Projectile Is Fired with an Initial Velocity Of v