math for the physics of a roller coasterA roller coaster cart of mass m = 339 kg startsstationary at point A, where h1 = 22.7 m anda while later is...

The question does not mention the direction of movement of
the roller coaster cart. We assume it to be in vertically downward
direction.

In this case the the speed of the cart is purely
due to acceleration due to gravity (g) as it falls from a height of 22.7 m to 7.1
m.

Thus the distance travelled by the cart
is

Distance = s = 22.7 - 7.1 =
15.6

We know that:

s =
(gt^2)/2

Where: t = time taken to move the distance s when
starting from velocity 0 and accelerating under the influence of g, the acceleration due
to gravity.

Substituting values of s and g in above
equation:

15.6 =
(9.8/2)t^2

t^2 = (15.6*2)/9.8 =
4

Therefor:

t = 4^(1/2) = 2
s

Thus the cart takes 2 seconds to reach the point
B.

The speed of the cart is then given
by:

Speed = g*Time

= 9.8*2 =
15.6 m/s

Answer:

Speed of cart
at B = 15.6 m/s