engineering science

a. By impulse = change of momentum

Ft = mv - mu

(1000)(0.1) = (2)(v - 0)

Initial velocity, v = 50 ms-1

So, by the law of conservation of energy,

Loss of K.E. = Gain of G.P.E.

1/2 mv2 = mgh

1/2 (50)2 = (10)h

Max. height, h = 125 m


b. By the equation of motion,

v2 = u2 + 2as

v2 = (50)2 + 2(-10)(0)

Final velocity, v = 50 ms-1 downwards.


c. Work done by the force = Gain in K.E. of the stone

= 1/2 mv2

= 1/2 (2)(50)2

= 2500 J


d. By the law of conservation of energy,

Loss of K.E. = Gain of G.P.E.

1/2 mu2 - 1/2 mv2 = mgh

1/2 (502 - v2) = (10)(50)

Velocity, v = 38.7 ms-1 or -38.7 ms-1

That is v = 38.7 ms-1 upwards or downwards

Or using equation of motion,

v2 = u2 + 2as

v2 = (50)2 + 2(-10)(50)

Velocity, v = 38.7 or -38.7

That is, v = 38.7 ms-1 upwards or downwards