Scientific measurement - 2 | Chemistry and the Scientific Method

What is the speed that must be given to a ball of mass 52 grams to go higher than a tree of 30 meters?

(Suppose there is no effect of air resistance).

At t = 0, the height = 0 m, so Ep0 = mgh = 0 J

At t = tf  (final time), the ball reaches the top of its trajectory 
⇒ the velocity = 0 m.s-1 
⇒ Ek tf = ½ mv2 = 0 J.
At this time we want h > 30 m, so Ep tf > 30 x m x g

Law of conservation of energy:
Etotal = cste = Ek + Ep = ½ mv2 + mgh
and Etotal (t = 0) = Etotal (t = tf)


Ek 0 = Ep tf > 30 x m x g
½ x m x v02 > 30 x m x g
v0 > (2 x 30 x g)0.5

v0 > 24 m.s-1