Question

erik’s 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 erik’s rocket above the ground over time?

Explanation:

Step1: Analyze the rocket's motion

The rocket starts on the ground (height = 0 at time = 0), moves up (height increases with time), reaches a peak, then comes back down (height decreases with time) until it hits the ground again (height = 0). The motion is a projectile motion, and the height - time graph should be a parabola (since the height \( h(t) \) of a projectile is given by a quadratic function \( h(t)=-gt^{2}+v_{0}t + h_{0} \), here \( h_{0} = 0 \), so \( h(t)=-gt^{2}+v_{0}t \), which is a parabola opening downwards).

Step2: Evaluate each graph

• First graph: It has a flat top, which would imply the rocket stops at a certain height, not realistic for a launched rocket (it should come back down).
• Second graph: The height increases and then stays constant, which is not correct as the rocket should fall back.
• Third graph: The height starts from a non - zero value (since it doesn't start at (0,0)) and then plateaus, incorrect.
• Fourth graph: It starts at (0,0) (height 0 at time 0), rises to a peak (parabola opening downwards) and then falls back to the ground (height 0 at some later time), which matches the motion of the rocket.

Answer:

The bottom - right graph (the parabola - shaped graph that starts at (0,0), rises to a peak, and then falls back to the ground)