If a Projectile Is Fired with an Initial Velocity Of v

question 133

Short Answer

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?