Determining speed and height on a roller coaster

[crushedcorn]

Homework Statement

One car (m=80.0 kg) tracks through the roller coaster in the following diagram. As it passes point A, it has a speed of 50.0 cm/s.

a) Determine the speed at points B, C, and E
b) If the speed at point D is _______, determine it's height (ignore friction)

Homework Equations

PE1 + KE1=PE2 + KE2
PE=mgy
KE=1/2mv^2

The Attempt at a Solution

a) I correctly got the velocity for point B as 44.3 m/s (1/2mv^2=mgy, 1/2(80 kg)v^2=(80kg)(9.80m/s^2)(100m). However, when I apply the same formula to points C and E my answer doesn't match that of the answer key.

Point C: (80 kg)(9.80 m/s^2)(38 m)=1/2(80 kg)v^2, v=27.3 m/s. Answer key answer: 34.9 m/s

Point E: (80 kg)(9.80 m/s^s)(20 m)=1/2(80 kg)v^2, v=19.8 m/s. Answer key answer: 39.6 m/s

b) 1/2(80 kg)v^2=(80 kg)(9.80 m/s^2)y. I can simplify this equation but I don't know how to solve this as I would have 2 variables that I need to solve for.

Thank you for your wonderful brains on this!

 

[jbriggs444]

You quoted the equation: PE1 + KE1 = PE2 + KE2
You used the equation: PE = KE

 

[Matternot]

Don't get confused with ΔPE=ΔKE

 

[crushedcorn]

PE1 + KE1=PE2 + KE2 becomes PE=KE because, for example, at point C KE1=0 and PE2=0, so I end up using the PE1=KE2 equation.

How am I confusing ΔPE with ΔKE?

 

[Matternot]

KE₁≠0 PE₂≠0

You haven't used the fact that it's moving at 0.5ms^-1 at A

You aren't confusing ΔKE with ΔPE. From your work it appears you are confusing ΔKE=ΔPE with KE=PE

 

[Matternot]

Total energy conserved:

mgy₁+1/2 mv₁²=mgy₂+1/2 mv₂²

For point B:
1/2(80kg)v²+(80kg)g0=(80kg)(9.80ms^-2)(100m)+1/2(80kg)(0.5ms^-1)²

The only reason you got the first part "right" is because 1/2(80kg)(0.5ms^-1) is really small compared to (80kg)(9.80ms^-2)(100m) and so it didn't make a noticable difference to the answer

 

[Matternot]

You want to use:

PE_A+KE_A=(80kg)(9.80ms^-2)(100m)+1/2(80kg)(0.5ms^-1)²=PE_x+KE_x=mgy+1/2mv²

For all but the last parts, y is known

For the last part, v is known