is the height of a ball be thrown directly related to the initial velocity? if i were to graph initial velocity as y and height as x,would it be a linear trend?
yes and yes
sorry. yes and no.
see
http://www.wolframalpha.com/input/?i=plot+x%3D10%2B5t-5t%5E2,+y%3D5-10t
Yes, the height of a ball thrown is directly related to the initial velocity. The initial velocity determines how high the ball will go and how long it will stay in the air.
If you were to graph the initial velocity as the y-axis and the height as the x-axis, the resulting graph would not show a linear trend. Instead, it would form a parabolic shape. This is because the height of the ball depends on the square of the time it spends in the air (since the acceleration due to gravity affects both the upward and downward motion of the ball). As a result, the relationship between the height and initial velocity is non-linear, and the graph would depict a parabolic curve.