Question

A projectile is shot at an angle of `pi/6` and a velocity of `3 m/s`. How far away will the projectile land?

Answer 1

Range `x=0.795329452" "`meters

Explanation:

Given `theta=pi/6`
initial velocity `v_0=3" "`m/sec

Compute the total time t it will be on the air

`y=v_0*sin theta*t+1/2*g*t^2`

`0=3*sin (pi/6)*t+1/2(-9.8)*t^2`

`0=3*(0.5)*t-4.9*t^2`

`0=1.5*t-4.9*t^2`

`0=t(1.5-4.9t)`

`t_1=0` and `t_2=1.5/4.9`

Let `x=`range

We will use `t_2=1.5/4.9`

`x=v_0 cos theta*t`

`x=3*cos (pi/6)(1.5/4.9)`

`x=0.795329452" "`meters

God bless....I hope the explanation is useful.