Help with AP Physics FRQ

A box is pressed against a horizontal spring, compressing the spring from its relaxed length. The box is then released and the spring launches the box horizontally along a track that ends in a ramp, as shown above. The box has enough speed to leave the ramp, and the box reaches a maximum vertical height above the oor. Assume there is negligible friction between the box and the track and air resistance is negligible. k is the spring constant of the spring. x is the distance the spring is compressed. M is the mass of the box. 6' (theta) is the angle of the ramp from the horizontal. h is the maximum height reached by the box. The scenario is repeated with the box compressing the spring a distance that is larger than the original distance x. (3) Indicate how it in this second scenario compares to h in the original scenario, and explain why without mathematically deriving a relation for h. (st 6)}: x2 W , which may or may not be correct. Is this equation consistent with your claim in part (3)? Explain why or why not. (b) Students derive an equation for the maximum height h in the original scenario, h = (g) Consider the system consisting of only the box, but not the spring or Earth. How does the energy of the system when the spring is fully compressed compare to the energy of the system at the moment immediately before the box hits the ground? Justify your answer. The angle of the ramp is changed such that it is larger than 6 but less than 90 degrees, while the height of the end of the ramp remains the same. (h) How would the maximum height of the box compare to the original scenario in which the ramp angle was equal to 6 ? Justify your answer. (i) Would the slope of the graph of vertical velocity as a function of time shown above part (c) be different for this scenario in which the box is launched from the larger angle? Justify your response. Vertical Velocity Time Two students, student 1 and student 2, are discussing the graph shown above, which shows the vertical component of the velocity of the box from when it leaves the ramp to immediately before it hits the oor. The students make the following statements. Student 1: This graph shows that the vertical acceleration of the box is constant, and that the box's speed decreases for the entire time shown. Student 2: The area between the graph and the time axis is the box's vertical displacement, but the graph is incorrect because the positive displacement should be equal to the negative displacement. (0) Which underlined phrase or phrases in student 1's statement are correct, if either? If neither phrase is correct, write \"none." ((1) Which underlined phrase or phrases in student 1's statement are incorrect, if either? If neither phrase is incorrect, write \"none.\" (e) Which underlined phrase or phrases in student 2's statement are correct, if either? If neither phrase is correct, write \"none." (0 Which underlined phrase or phrases in student 2's statement are incorrect, if either? If neither phrase is incorrect, write \"none.\