Graph a thrown object given angle and force

Question

What is the equation for the graph of a thrown object (if it is thrown from the origin, ignoring air resistance), given its angle of elevation and throwing force (both constants)?

Answer 1

When air resistance is neglected, the vertical and horizontal components of motion can be treated separately. If the vertical component is $y=v_0 t + \frac 1 2 a t^2$ (where $a$ is a negative quantity, the acceleration of gravity), and the horizontal component is $v_1 t,$ then one can write $x=v_1 t,$ so $t= x/v_1,$ and use that to find the height $y$ as a function of $x.$

"Throwing force" is insufficient information unless you know the mass of the object and the time the force is applied. Initial speed would be enough. If you know the angle of elevation and the initial speed, you can find the vertical and horizont components of initial velocity, $v_0$ and $v_1,$ by using trigonometry.