A projectile is launched from ground level at an angle of 35 degrees above the horizontal line (x-axis??) with an initial velocity of 65m/s. Determine the time when |v|=58m/s

Question

anonymous · Answer

Here's one way you could solve it -
Firstly you need to consider the horizontal and vertical components of the velocity separately.
The horizontal motion has no acceleration.
The vertical motion has the acceleration due to gravity, g.
Write down expressions for each component of the velocity as a function of time.
Then you can use the expression
$$v^2=v _{x}^2+v _{y}^2$$
to get an equation relating v and t.
You should end up with a quadratic equation for t.

anonymous · Answer

and bonus question

when u solve the quadratic equation.. 

you ll get two answers (both positive) ... can u think WHY you get two answers??


and 
bonus question 2

for one particular value of |v|.. the quadratic equation will be a perfect square and yield one answer only.  Again can u think.. why would it be that? (also can u find what that |v| is and what that time is?) ;-)