A projectile is shot at an angle of #pi/6 # and a velocity of # 3 2 m/s#. How far away will the projectile land?

1 Answer
Jul 12, 2016

#x_m=90.40" "m#

Explanation:

enter image source here
#"please look over the animation carefully"#
#"The initial velocity of object can be split into two components"#
#"as vertical and horizontal. "(v_x,v_y)#

#v_x=v_i*cos alpha#
#v_y=v_i*sin alpha-g*t#

enter image source here

#"we can find the time elapsed using the component "v_y#

#"we can write "v_y=0 " for the maximum height."#

#v_y=v_i*sin alpha-g*t=0#

#v_i*sin alpha=g*t#

#t=(v_i*sin alpha)/g#

#t_f:"represents the flaying time"#

#t_f=2*t=(2*v_i*sin alpha)/g#

enter image source here

#x_m=v_x*v_f#

#x_m=(v_i*cos alpha*2*v_i*sin alpha)/g#

#x_m=(v_i^2*2*sin alpha*cos alpha)/g#

#2*sin alpha*cos alpha=sin 2 alpha#

#x_m=(v_i^2*sin 2alpha)/g#

#"where:"#
#v_i=32" "m/s#
#2*alpha=pi/6*2=pi/3#
#g=9.81" "m/s^2#

#x_m=(32^2*0.866)/(9.81)#

#x_m=90.40" "m#