# 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?

##### 1 Answer

#### Explanation:

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:

where:

#(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:

#v_(0x)=v_0cosalpha#

#v_(0y)=v_0sinalpha#

(#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.

Let's find

To find the range we can assume:

**is** the range!), so:

(using the double-angle formula of sinus).

Now we have the *right* formula to answer the question:

and (the sinus has supplementary solutions):