Question

A particle slides back and forth on a frictionless track whose height as a function of horizontal position is given by y = ax^2, where a = 0.80 m-1 If the particle's maximum speed is 8.5 m/s , find the turning points of its motion Express your answer using two significant figures. Please round to two sig figs in a x1,x2 format

Answer 1

y = ax² = parabola path(frictionless)

At highest point, the velocity is 0 m/s. kinetic energy at the highest point = 0 J.

mgh = ½ m v²

g h = ½ v²

9.81 * h = ½ * 8.5²

h = 36.125/9.81

h = 3.68 m = ‘y’coordinate of the highest point.
y = 0.80*x²

and

y = ax²

3.68 = 0.80*x²

x² = 4.603083

x = ±2.14 = ‘x’coordinate of the highest point.

2 turning points = (3.68, 2.14) and (3.68, -2.14)