Trouble visualizing 2D vector problem? Fireworks are fired at an angle of $82$ degrees from the horizontal. The technician expects them to explode $100$ m in the air $4.8$s after they are fired. Find initial velocity?
How do i find initial velocity fired from ground level?
is $4.8$ s my horizontal, and $100m$ my vertical and is this just a right angle triangle where initial velocity is my hypotenuse?
thanks!
 A: 
The diagram is a rough sketch. Your comment about sohcahtoa hints this may be a straightforward question involving no acceleration (see part 1) else its a high-school type physics problem (see part 2)

*

*Assuming no acceleration, initial velocity=final velocity. Hence using $speed=\dfrac{distance}{time}$, where distance can be calculated using the triangle in the diagram.


*assuming acceleration due to gravity=$g$: considering vertical velocities $v=u\sin 82^o+at=u\sin 82^o-4.8g \ $ and $v^2=(u\sin 82^o)^2-2gs=(u\sin 82^o)^2-200g$. Using these equations, $u\approx 44.81 \text{ms}^{-1} \text{for $g$=9.81}$
note: I have not considered the case where the firework reaches maximum height and then explodes during descent since then the data provided in the question would be insufficient.
A: The fact that you posed your questions as a simple "2-D Vector Problem" hints to me that we shouldn't be worried about gravity. Think of your firework in outer space, away from the influence of gravity. Thus, your projectile is moving with constant velocity in all dimensions.
The initial velocity vector you wish to find will have two components, one vertical and one horizontal (both will be speeds in units of $m/s$). You have been given two pieces of information: the initial angle of firing, and the vertical distance covered by the projectile in 4.8s. 
Now, visualize your problem as follows. The vertical component of the initial velocity will be the vertical distance travelled in 4.8s. The horizontal component will be the product of your initial velocity $v_0$ and the cosine of 82 degrees. 
Once you have done this, consider how you can combine these two facts to solve for $v_0$. (Hint: there is a function which relates the sides opposite and adjacent to a given angle).
