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.

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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.

1 Answer
ali ergin
Feb 15, 2018

#"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#

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