When a ball is thrown upwards, it follows a curved path known as a parabola. This is due to the effect of gravity acting on the ball after it is thrown. The equation s = -10t² + vt + k describes the height (s) of the ball at any time (t) in seconds, where v represents the initial velocity in meters per second and k is the ball’s initial height.
The term -10t² indicates that the force of gravity, which accelerates the ball downwards at a rate of approximately 10 meters per second squared, is constantly pulling the ball down. This downward acceleration causes the ball to slow down as it rises until it reaches its highest point, before it starts to descend. The vt term accounts for the initial upward motion, while k represents where the ball began its journey.
Thus, the combination of these components gives rise to a parabolic trajectory. The upward motion creates one side of the parabola, and the downward pull of gravity creates the other. This is why when you graph the height of the ball over time, you observe a nice, smooth curve characteristic of a parabola.