A ball rolling up a parabolic ramp
Hi guys! I'm Alan and I'm new here. I hope that we will discuss physics problem solving and concepts freely.
Today I need some help with this problem:
Assume there is gravity, no friction and no external force acting on the system. A ball has an initial velocity of 5 m/s and climbs up a parabolic ramp, which is defined by y=(x^2)/3. If the ball rolls exactly along the path of ramp, starting from (0,0), calculate the time taken for the ball to climb to a height of y=1.
I solved it using differential equations but the differential I got is only numerical integratable (results given by wolfram alpha). I'm looking for an easier way to solve this problem. So, guys, please help! Thanks!
