Question

Problem #1) remember nach a A roller-coaster reaches a velocity of 30 meters/sec. It also has an acceleration of 10 meters/sec in the direction of motion. If the radius of curvature at this point is 50 meters, Calculate the acceleration of the roller-coaster at this point.

Answer 1

Velocity of the roller coaster = V = 30 m/s

Acceleration of the roller coaster in the direction of motion = Tangential acceleration = a_t = 10 m/s²

Radius of curvature at this point = R = 50 m

Radial acceleration of the roller coaster = a_r

a_r = V²/R

a_r = (30)²/50

a_r = 18 m/s²

Acceleration of the roller coaster = a

$a = \sqrt{(a_{r})^{2} + (a_{t})^{2}}$

$a = \sqrt{(18)^{2} + (10)^{2}}$

a = 20.59 m/s²

Acceleration of the roller coaster at this point = 20.59 m/s²