Question

eriks physics class is outside testing the miniature rockets they built. erik sets his rocket on the ground and then launches it into the sky. it shoots up high in the air before returning to the ground. which graph could show the height of eriks rocket above the ground over time?

Explanation:

Step1: Analyze the motion of the rocket

When the rocket is launched, it first accelerates upwards (height increases with time). Then, due to gravity, its upward velocity decreases until it reaches the maximum height (where the slope of the height - time graph is zero). After that, it starts to fall back down (height decreases with time).

Step2: Consider the shape of the graph for each option

• The second graph (with a horizontal asymptote) implies that the rocket reaches a certain height and then stays at that height forever, which is not the case as the rocket will fall back to the ground.
• The third graph (a triangular - like shape) implies a constant acceleration upwards and then a constant deceleration (with the same magnitude) which is not realistic for a rocket's motion (in reality, the acceleration due to gravity is constant, and the rocket's engine provides an initial thrust).
• The fourth graph (a step - like shape) implies an instantaneous increase in height and then no change, which is not physical.
• The first graph (a curve that first rises, then falls) is consistent with the motion of an object under the influence of an initial upward force (from the rocket's engine) and then gravity (as it falls back). In a simple model, the height \(h\) of an object in vertical motion (neglecting air resistance and considering a constant acceleration due to gravity \(g\)) is given by the quadratic function \(h(t)=v_0t-\frac{1}{2}gt^{2}\) (where \(v_0\) is the initial velocity), which has a parabolic shape.

Answer:

The first graph (the one with a parabolic - like shape).