The discussion revolves around a problem related to projectile motion, specifically focusing on the use of a column vector and a scalar multiplier in the context of velocity and displacement vectors.
Some participants have provided insights into the relationship between the velocity vector and the displacement vector OB, noting that the velocity must be a constant multiple of the displacement. There are multiple interpretations of the role of h, with some suggesting it is necessary for unit consistency while others express confusion about its application in subsequent calculations.
There appears to be some ambiguity regarding the notation used in the problem, with participants noting a potential misinterpretation of the variable h as u. Additionally, the relevance of h in later steps of the calculations is questioned, indicating a need for further clarification on its application.
Delphi51 said:I'm glad you said it was an "h"; looked like a "u" to me which would really be mysterious.
He is just saying the velocity vector must be a constant times the displacement vector OB. Same as saying the ratio of the vertical to the horizontal must be the same for the displacement and the velocity in order for them to have the same slope and be parallel. The h just takes care of the units so h*(50 meters) = 10 m/s
Funny, the h doesn't seem to be used in the following steps. I would have followed up the
velocity vector = [Vx,Vy] = h[50, -52.5]
with [10, 14 - gt] = [50h, -52.5*50h]
and then 10 = 50h so h = 0.2 and 14 - gt = -52.5*50h
which solves to t = 2.5.
Alternatively, slope of OB = = slope of trajectory at time t
Dy/Dx = Vy/Vx
-52.5/50= (14- gt)/10
-525/50 = 14 - gt
gt = 14 +525/50 = 24.5
t = 24.5/g = 2.50.