Question

A projectile is shot from the ground at a velocity of `29 m/s` and at an angle of `(2pi)/3`. How long will it take for the projectile to land?

Answer 1

`x=74.24" m"`

Explanation:

`"The velocity of projectile can be split two components as vertical and horizontal"`

`"the vertical component can be calculated using the formula:"`
`v_y=v_i*sin alpha-g*t" "figure" "1`

`"you are seeing how the vertical component of velocity is changing "`

`"please note that the vertical component of velocity " v_y" is zero at maximum height"`

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

`"2*t gives us the traveling time"`

`color(red)(t_t=(2*v_i*sin alpha)/g)`

`"the object is conveyed by the horizontal component of velocity "v_x" figure 3"`

`"the horizontal component of velocity is calculated by:"`

`color(green)(v_x=v_i*cos alpha)`
`"the horizontal component of velocity doesn't change"`

`"and doesn't depend on time"`

`"the horizontal position of object can be calculated by:"`

`x=color(green)(v_x)*color(red)(t)`

`x=color(green)(v_i*cos alpha)*color(red)(t)`

`"now; we can write "color(red)(t=t_t)`

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

`"so "2*sin alpha*cos alpha=sin(2 alpha)`

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

`"where "v_i=29" m/s"" "alpha=((2pi)/3)`

`x=(29^2*sin(2*(2pi)/3))/(9.81)`

`x=(841*0.866)/(9.81)`

`x=74.24" m"`