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

Question

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.

Adrian Ayala · Accepted Answer

#"please check math operations."#

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

(two v_i sin(theta))/g# = #t

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

#t=20.39 seconds.#

# "The horizontal component of initial velocity :" #

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

#"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#

#2*a*t^2# #"y_range:"

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

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

# "impact velocity:" #

# "It falls at a speed of 200" meters per second "in the east direction." #

200 ms^-1 #v_("east")

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

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

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

#v=204.12 " "ms^-1#

Adam Arnold · Answer

undefined The landing location of the projectile is determined by other factors like the initial height and gravity, which are not provided. The speed of impact can be calculated, but I would need additional information.