how do u go about solving this? physics? a roller coaster reaches the top of the steepest hill with a speed...

Question

a roller coaster reaches the top of the steepest hill with a speed of 6 km/h. It then descends the hill, which is at an average angle of 45 degrees and is 45.0 m long. What will its speed be when it reaches the bottom. Assume (mu)k = 0.12

answer: 23 m/s (85 km/h)

Answer 1

EDIT: Note corrected formula (numeric answer is the same)

If you assume the coaster ends up moving horizontally, then you need to find the speed contributed by the fall in altitude plus the contribution from initial horizontal velocity.

The speed from the fall is obtained from conservation of energy: the total energy at the top of the hill is the potential energy from the height plus the kinetic energy of the speed:

m*g*h + 0.5*m*vh^2,

where h = height, vh = horizontal velocity at top. This energy, less frictional loss is converted to kinetic energy at bottom,

0.5*m*v^2

Energy lost to friction is Fr*L, where Fr is the frictional force and L the length of travel. The frictional force is µ*Fn, where Fn = normal force; Fn = m*g*sinø, where ø = 45º. The frictional loss is then

µ*m*g*L*cosø ........(EDIT: changed from sinø)

put it all together to get

m*g*h + 0.5*m*vh^2 - m*µ*g*cosø = 0.5*m*v^2

v = √[2*g*h - 2*µ*g*L*cosø + vh^2]

h is the side of a right triangle with hypotenuse L and angle opposite = 45º; therefore h = L *sinø

v = √[2*g*L*(sinø - µ*cosø) + vh^2]

Solve for v; remember, if you use g = 9.8 m/sec^2 and h in meters, the result will be m/sec, so convert vh = 6 km/hr to m/sec,

Answer 2

it's physix allrite.

use energy conservation

potential energy = mgh
kinetic energy = 1/2 m v^2

find the difference in elevation at the bottom, that's how much potential energy decreases by.

some of this goes into friction = Fdistance = N*mu_k*distance

rest goes into kinetic energy

voila, hope it helps