Question

What is the landing location of the projectile and its speed of impact?

A projectile of mass 1 kg is launched from ground level toward the east at 200 m/s, at an angle of `pi/6` to the horizontal. If the spinning of the projectile applies a steady northerly Magnus force of 2 newtons to the projectile.

~~~~~~~~~~~

The answer is Landing point: (3534.8,416.5,0) and Speed at impact: 204 m/s, but i don't know how to start the problem.

Answer 1

`"please check math operations."`

Explanation:

`"The projectile will do a three dimensional motion. while"`
`"projectile is moving to eastward with horizontal component of "`
`"its velocity, the Force of 2N moves it toward north."`

`"The time flight for the projectile is:"`

`t=(2 v_i sin(theta))/g`

`t=(2*200*sin (30))/(9.81)`

`t=20.39 sec.`

`"The horizontal component of initial velocity :"`

`v_x=v_i*cos 30=200*cos 30=173.21 " "ms^-1`

`"x-range :" =v_x*t=173.21*20.39=3531.75 " "m`

`"the force with 2N causes a acceleration toward north ."`

`F=m*a`

`2=1*a`

`a=2 ms^-2`

`"y_range :" 1/2*a*t^2`

`"y-range :"=1/2*2*(20.39)^2`

`"y-range :"=415.75" "m`

`"impact velocity:"`

`"It falls at a speed of 200 " m s^-1 " in the east direction."`

`v_("east")=200 ms^-1`

`v_("north")=a*t=2*20.39=40.78" "ms^-1`

`v=sqrt(v_("east")^2+v_("north")^2)`

`v=sqrt(200^2+(40.78)^2)`

`v=204.12 " "ms^-1`