Answer
The motorcyclist will emerge from the sandy stretch with a speed of 14 m/s.
Work Step by Step
We can use a force equation to find the acceleration.
$ma = F_f$
$ma = mg ~\mu$
$a = g ~\mu = (9.80 ~m/s^2)(0.70) = 6.86 ~m/s^2$
The can use this rate of deceleration to find the speed after 15 meters:
$v^2 = v_0^2 + 2ax$
$v = \sqrt{v_0^2 + 2ax}$
$v = \sqrt{(20.0 ~m/s)^2 - (2)(6.86 ~m/s^2)(15 ~m)}$
$v = 14 ~m/s$
The motorcyclist will emerge from the sandy stretch with a speed of 14 m/s.