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
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