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Using standard formulae, derive an expression for the final speed of a falling object in terms of its change in height. Assume zero air resistance or other resistive forces.

E k = (1/2)mv 2 E p = mg(dh) Set these equal to each other, because of conservation of energy: (1/2)mv 2 = mg(dh) Cancel the mass: (1/2)v 2 = g(dh) v 2 = 2g(dh) v = (2g(dh)) 1/2
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Answered by Danny L. • Physics tutor
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Why do metals conduct electricity?

To answer this question we need to think about the bonding that occurs within metals. Metallic elements form strong lattices due to the metallic bonding. This consists of a lattice of positive metal atoms. T...
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Answered by Alex M. • Chemistry tutor
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I want to pave my patio, which has dimensions of 6m by 8m. I'm going to pave it with stones that have dimensions of 50cm by 50cm. Each tile costs £1.50. How much will paving my patio cost me?

My patio has an area of 6 8 m , so 48m 2 . Each tile has an area of 0.5 0.5 m, so 0.25m 2 . To find the number of tiles we need, we divide the area of the patio by the area of one tile: 48/0.25 = 192 tiles E...
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Answered by Danny L. • Maths tutor
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Integrate ((5x^3) + ((2x)^-1) + (e^2x))dx.

int(5x 3 + (2x) -1 + e 2x )dx =int(5x 3 )dx + int((2x) -1 )dx + int(e 2x )dx int(5x 3 )dx = (5/4)x 4 + c where c is the constant of integration int(2x -1 )dx = (1/2)ln(2x) + d where d is another constant of ...
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Answered by Danny L. • Maths tutor
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Fully simplify (8a^2b * ab^4)/(2a^3b^2)

8a 3 b ab 4 2a 3 b 2 (can write this more clearly by hand using whiteboard) First go about seperating and collecting terms. Begin with the top line. 8 remains the same as there are no other known numbers. We...
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Answered by Archie I. • Maths tutor
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