# If a projectile is shot at a velocity of 3 m/s and an angle of pi/3, how far will the projectile travel before landing?

Jun 26, 2018

Approximately $0.8$ meters.

#### Explanation:

I assume that the projectile was launched from flat ground.

Range of a projectile is given by the equation:

$d = \frac{{v}^{2} \sin \left(2 \theta\right)}{g}$

where:

• $d$ is the total distance traveled

• $v$ is the initial velocity

• $\theta$ is the angle of incline

• $g$ is the gravitational acceleration, which is $9.8 \setminus {\text{m/s}}^{2}$ on Earth

So, we get:

d=((3 \ "m/s")^2*sin((2pi)/3))/(9.8 \ "m/s"^2)

$= \left(9 \setminus {\text{m"^2"/s"^2*0.87)/(9.8 \ "m/s}}^{2}\right)$

=(7.83color(red)cancelcolor(black)"m"^2"/"color(red)cancelcolor(black)("s"^2))/(9.8color(red)cancelcolor(black)"m""/"color(red)cancelcolor(black)("s"^2))

$\approx 0.8 \setminus \text{m}$