Question

If a projectile is shot at a velocity of `21 m/s` and an angle of `pi/6`, how far will the projectile travel before landing?

Answer 1

`x_m=38,93 m`

Explanation:

`v_i=21 m/s`
`alpha=pi/6`

`v_y=v_i*sin alpha-g*t`
`v_y=0 " maximum height"`
`0=v_i*sin alpha-g*t`

`g*t=v_i*sin alpha`

`t_m=(v_i*sin alpha)/g" elapsed time to the maximum height"`

`t_e=2*t_m" traveling time"`

`t_e=(2*v_i*sin alpha)/g`

`v_x=v_i*cos alpha`

`x_m=v_x*t_e`

`x_m=v_i*cos alpha*2*(v_i*sin alpha)/g`

`2*sin alpha*cos alpha=sin 2 alpha`

`x_m=(v_i^2*sin 2 alpha)/g`

`x_m=(21^2*sin 2*pi/6)/(9,81)`

`x_m=38,93 m`