# A roller coaster has a hill that is #20m# tall. If the roller coaster cart is moving at #20m/s# as it enters the bottom of the hill, how do you answer the following questions?

##
a) Will it make it all the way over the hill? (assume no friction)

b) If the roller coaster cart had a mass of #5000kg# and friction does #80kJ# of work on the cart, how high up the hill does the cart go?

a) Will it make it all the way over the hill? (assume no friction)

b) If the roller coaster cart had a mass of

the answer to (a) is yes and (b) is 18.76m (both assuming

For part (a) we are to assume no friction. Hence all kinetic energy will be converted to potential energy.

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Sure, I can help. Please go ahead and ask the specific questions you have about the roller coaster scenario.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- The force applied against an object moving horizontally on a linear path is described by #F(x)= cospix+3x #. By how much does the object's kinetic energy change as the object moves from # x in [ 1, 2 ]#?
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- A car is traveling with a velocity of 30 m/s has a kinetic energy of 800,000 J. What is the mass of the car?

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