Suppose that you launch a projectile at a high enough velocity that it can hit a target at a distance. Given the velocity is 34-m/s and the range distance is 73-m, what are two possible angles the projectile could be launched from?
The motion is a parabolic motion, that is the composition of two motion:
the first, horizontal, is an uniform motion with law:
and the second is a decelerated motion with law:
#(x,y)#is the position at the time #t#; #(x_0,y_0)#is the initial position; #(v_(0x),v_(0y))#are the components of the initial velocity, that are, for the trigonometry laws:
#alpha#is the angle that the vector velocity forms with the horizontal); #t#is time; #g#is gravity acceleration.
To obtain the equation of the motion, a parabola, we have to solve the system between the two equation written above.
To find the range we can assume:
(using the double-angle formula of sinus).
Now we have the right formula to answer the question:
and (the sinus has supplementary solutions):