Answer
(a) The speed of the paper relative to the ground is $13.0~m/s$
(b) The speed of the paper relative to the ground is $3.0~m/s$
(c) The speed of the paper relative to the ground is $9.4~m/s$
Work Step by Step
Let $v_{p,g}$ be the velocity of the paper relative to the ground.
Let $v_{p,b}$ be the velocity of the paper relative to the bike.
Let $v_{b,g}$ be the velocity of the bike relative to the ground.
(a) We can find the velocity of the paper relative to the round:
$v_{p,g} = v_{p,b}+ v_{b,g}$
$v_{p,g} = 8.0~m/s+ 5.0~m/s$
$v_{p,g} = 13.0~m/s$
The speed of the paper relative to the ground is $13.0~m/s$
(b) We can find the velocity of the paper relative to the round:
$v_{p,g} = v_{p,b}+ v_{b,g}$
$v_{p,g} = -8.0~m/s+ 5.0~m/s$
$v_{p,g} = -3.0~m/s$
The speed of the paper relative to the ground is $3.0~m/s$
(c) We can use the Pythagorean theorem to find the speed of the paper relative to the ground:
$v_{p,g} = \sqrt{(5.0~m/s)^2+(8.0~m/s)^2}$
$v_{p,g} = 9.4~m/s$
The speed of the paper relative to the ground is $9.4~m/s$
