A roller coaster travelling towards the right has a speed of 30 m/s at the top o

Question

A roller coaster travelling towards the right has a speed of 30 m/s at the top of hill B which is 35.714 m above the ground level represented by points A, C and E. The height of hill D above the ground level is 100 m. Ignore friction or other losses and assume conservation of energy.

Use g = 9.80 m/sec2.                                    

   (a) What was the speed of the coaster at A?

   (b) Can the coaster climb to the top of hill D? If so, what will its speed be there?

3.) A roller coaster travelling towards the right has a speed of 30 m/s at the top of hill B which is 35.714 m above the ground level represented by points A, C and E. The height of hill D above the ground level is 100 m. Ignore friction or other losses and assume conservation of energy. Use g -9.80 m/sec2. (a) What was the speed of the coaster at A? (b) Can the coaster climb to the top of hill D? If so, what will its speed be there? (b) If you find the coaster cannot climb to the top of hill D, what is the maximum height to which it can climb on hill Dbefore it rolls back to the left?

Explanation / Answer

a)

We will apply law of conservation of energy,

MEB = MEA

PEB+KEB = KEA

mghB + ½*m*vB2 = ½*m*vA2

ghB + ½*vB2 = ½*vA2

9.8*35.714+1/2*30^2 = ½* vA2

vA =40m/s

b)

We will apply law of conservation of energy,

PED = MEA

mghD = mghA+ ½*m*vA2

ghD = ghA+ ½*vA2

9.8*100 > 9.8*35.714+1/2*30^2

Thus MEA < PED

Roller coaster can’t climb top of the hill D.

c)

PED = MEA

mghD = mghA+ ½*m*vA2

ghD = ghA+ ½*vA2

9.8*hD= 9.8*35.714+1/2*30^2

hD= 81.6m

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