Standing Vertical Jumps – Sports Physics with a Smartphone

Abstract

The standing vertical jump (SVJ) is a classical topic in Newtonian mechanics (Fig. 1). Although the topic has also been treated by others (other terms used are “standing high jump” or “squat jump”), the present paper shows how a smartphone can be used to capture video of a jump and determine the jump height. A crucial assumption often made in analysis of the SVJ is the constancy of force or acceleration during the stand-up phase. This is, however, not a trivial assumption in view of the changing geometrical configuration of the legs during standing up. We show that indeed the acceleration of the center of mass is nearly constant during the stand-up phase of the jump, a finding that has so far only been possible by much more expensive measurements (force plates).