Hungry Tommy !!!

Classical Mechanics Level 2

Tommy, the cat at A A is very hungry now and it needs some food which is at C C . So, it starts sliding from rest at A A and reaches B B from where it gets projected horizontally towards point C C . Given that A A and B B are at heights 10 m, 8 m \text{10 m, 8 m} respectively and the horizontal distance between B B and C C is 10 m \text{10 m} . Can Tommy get his food?

Assumptions : All surfaces are friction-less. Tommy gets projected only horizontally at B B and not at any angle. Also, he will stop where he lands and will not move further.

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Ram Mohith by Ram Mohith , 18, India

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1 solution

Ram Mohith
Sep 27, 2018

First, we will find with what velocity will Tommy reach B B . As it starts from rest initial kinetic energy is zero. Let us assume Tommy is of mass m m . P . E A = K . E B + P . E B m ⋅ g ⋅ 10 = 1 2 ⋅ m ⋅ v 2 + m ⋅ g ⋅ 8 v 2 = 4 g ⟹ v = 2 g \begin{array}{c}~ P.E_{A} = K.E_{B} + P.E_{B} \\ m \cdot g \cdot 10 = \dfrac12 \cdot m \cdot v^2 + m \cdot g \cdot 8 \\ v^2 = 4g \implies \boxed{v = 2 \sqrt{g}} \\ \end{array} As, Tommy gets horizontally projected from B B with velocity v v and from height 8 m 8~m the horizontal range is given by : R = v ⋅ 2 h g R = 2 g ⋅ 16 g = 2 ⋅ 4 = 8 m \begin{array}{c}~ R = v \cdot \sqrt{\dfrac{2h}{g}} \\ R = 2 \sqrt{g} \cdot \dfrac{\sqrt{16}}{\sqrt{g}} = 2 \cdot 4 = 8~m \\ \end{array} According to the given condition the food is 10 m 10~m from B B but Tommy can reach only 8 m 8~m . So, it cannot reach the food at C C .

6 Helpful 0 Interesting 0 Brilliant 0 Confused

You claimed that the surfaces are frictionless. Therefore, Tommy will slide all the way to the food after he lands 8 feet from B B .

Blan Morrison - 2 years, 8 months ago

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Ok. It is slightly confusing. However, I have edited the question for more clarity. Thank You !!!

Ram Mohith - 2 years, 8 months ago

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I made the same mistake - it's definitely not helpful to say "all surfaces are frictionless" at the start and then change that at the end! (Incidentally, an alternative but similar problem could have the food too close to the wall for Tommy to get)

Chris Lewis - 1 year, 7 months ago

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