AP EAPCET 08-Jul-2022 Shift 2 Paper

89. (c) We know that, coefficient of restitution,
e=(

Relative‌v‌e‌l‌o‌c‌i‌t‌y‌o‌f‌s‌e‌p‌a‌r‌a‌t‌i‌o‌n

Relative‌velocity‌of‌approach

)
Now, given collision is as shown

As impact is along normal to surface it does not change the horizontal component of ball.

Now if v2y is final vertical component then
v2y=e⋅v1y=0.2×5‌cos‌60∘
or v2y=0.2×5×

1

2

=0.5m∕ s
So components of final velocity of ball are
v2x=v1x=5sin60∘=(5√3)∕2
and v2y=e.v1y=1∕2
Hence, final speed of ball, vf=√(v2x)2+(v1x)2
‌=√(

5√3

2

)2+(

1

2

)2
=√

75

4

+

1

4

=√

76

4

=√19m∕ s