Final answer:
The time required for the penguin to slide to a halt on the horizontal patch of ice cannot be calculated due to the absence of acceleration. Therefore, the correct option is D. 4.6 s.
Step-by-step explanation:
To determine the time required for the penguin to slide to a halt on the horizontal patch of ice, we need to consider the forces acting on the penguin as it slides down the incline. The force of gravity acting parallel to the incline is mg*sin(angle), and the force of kinetic friction opposing the motion is μ*mg*cos(angle), where mg is the weight of the penguin, angle is the angle of the incline, and μ is the coefficient of kinetic friction.
Since the penguin is sliding at a constant velocity, the net force on the penguin is zero. Therefore, mg*sin(angle) = μ*mg*cos(angle). We can cancel out the mass to get sin(angle) = μ*cos(angle). Solving for μ, we find that μ = tan(angle).
Using the given angle of 6.9°, we can calculate the coefficient of kinetic friction to be approximately 0.119. Now, to find the time required for the penguin to slide to a halt on the horizontal patch of ice, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Since the penguin is sliding at a constant velocity, the acceleration is zero. Therefore, the time required for the penguin to slide to a halt is t = (v - u)/a = (0 - 1.4 m/s)/0 = 0/0.
Since the denominator is zero, the equation is undefined and we cannot calculate the time required for the penguin to slide to a halt. Therefore, the correct option is D. 4.6 s.