Shows the potential energy of a 500
g
particle as it moves along the
x
-axis. suppose the particle's mechanical energy is 12
j
.

figure
1 of 1
the figure shows the potential energy of a particle moving along the x-axis. the energy is measured in joules. there is a linear vertical potential barrier at x equal to 1 meter. for x from 1 to 4 meters the energy linearly increases from 2 to 8 joules. for x from 4 to 6 meters the energy linearly decreases to 0. for x from 6 to 8 meters the energy linearly increases to 12 joules and keeps growing for further distances.

part a
where are the particle's turning points?
express your answer using two significant figures. enter your answers in ascending order separated by commas.

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.