A truck starts from rest at the top of a uniform slope and coasts down it a distance of 175 m, as a result its height above the ground is reduced by 59.1m. The plane is frictionless. What is the trucks velocity when it reaches the 175m mark, and how long does it take to reach this mark?
answer: 34.0ms^1 and 10.3 s.
Not quite sure how to do this question. I created a triangle with a hypotenuse of a and opposite side of 9.8 due to gravity, but didn't get the right answer.
Hey Chloe! No worries, I'll step through it for you!
So, rather than being a question on forces, acceleration and the like, this is actually a very deceitful question on
conservation of energy. Say what?
EDIT: RuiAce has a solution below, which resolves forces to obtain the solution to Part B first, then Part A. Both are correct, use whichever seems simpler to you
So, the truck starts from rest at the top of the hill. At this stage, the energy possessed by the truck is equal to the gravitational potential energy, which can be expressed as the product of its mass, its height, and the acceleration due to gravity. That is:
There is some things here we don't know, but bear with me.
Now, once the truck hits the 175 metre mark, the truck has two types of energy. It has potential energy like before, at a new height which is 59.1 metres less than the initial height. It also has kinetic energy. We can express this as:
+\frac{1}{2}mv^2 )
Now, the conservation of energy says that the energy of the truck must be conserved. The question specifies that the plane is frictionless, so we know that no energy is lost to friction. In Tertiary Physics, we call this a
conservative system. So, we can equate the two expressions for energy and solve for the velocity (we will find lots of cancellation):
 + \frac{1}{2}mv^2 \\ gh = gh - 59.1g +\frac{1}{2}v^2 \\ \frac{1}{2}v^2= 59.1g \\ v = \sqrt{2\times59.1\times9.8} \approx 34.0ms^{-1} )
So that is Part A! For Part B, we know the final velocity, and we can use this to calculate the acceleration of the truck as it rolls (it will be constant since gravity is the cause, the only reason we can't use gravity directly is because it is on an incline). We use the following formula from the formula sheet:
And thus we can find the time taken:
Note that there is a few ways to do Part B, but this is my preferred method due to its simplicity.
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