Question : A ball is dropped from a height of 5 metre on a plane. On bouncing, it rises to a height of 1.8m. Calculate the fractional loss of velocity of ball. The value of g is not known.
Doubt by Zoha
Solution :
Case I : When the ball is dropped and goes from top to bottom then
Initial velocity, u = 0
Final Velocity, v =?
Displacement covered by Ball (Height)=h=5m
Using 3rd Equation of Motion
V²-u²=2as
v²-(0)²=2(+g)h
v²=2gh
v=√(2gh) — (1)
Case 2 : When the ball is bounced back and move from bottom to the top then
Initial velocity, u' = ?
Final Velocity, v = 0
Displacement covered by Ball (Height)=h'=1.8m
Using 3rd Equation of Motion
v'²-u'²=2as
v'²-u'²=2(-g)h'
0²-u'²=-2gh'
-u'²=-2gh'
u'=√(2gh') — (2)
Fractional loss of velocity
= (Change in Velocity)/Initial velocity
= (u'-v)/v
= u'/v-v/v
= u'/v-1
= √(2gh')/√(2gh) - 1
= √[(2gh'/2gh)]-1
= √[h'h]-1
= √[1.8/5] - 1
= √[0.36] -1
= 0.6-1
= -0.4
The -ve sign shows that velocity is decreasing.
Required fraction loss of velocity is 0.4 or 4/10 or 2/5.