Doug hits a hockey puck, giving it an initial velocity of 6.0 m/s. If the coefficient of kinetic friction between ice and puck is 0.032, how far will the puck slide before stopping?

A) 19 m
B) 25 m
C) 37 m
D) 57 m
E) 68 m

D- 57 m

To determine how far the puck will slide before stopping, we need to calculate the deceleration of the puck due to friction and then use the equations of motion to solve for the distance.

The deceleration of the puck can be calculated using the equation:
a = μ * g,
where a is the deceleration, μ is the coefficient of kinetic friction, and g is the acceleration due to gravity.

Given:
Coefficient of kinetic friction (μ) = 0.032
Acceleration due to gravity (g) = 9.8 m/s^2

Plugging in the values, we find:
a = 0.032 * 9.8
= 0.3136 m/s^2

We can use the equation of motion to solve for the distance traveled (d) by the puck before stopping:
v^2 = u^2 + 2a * d,
where v is the final velocity, u is the initial velocity, a is the deceleration, and d is the distance traveled.

Since the puck stops, the final velocity (v) is 0.

Plugging in the values, we have:
0^2 = 6^2 + 2 * 0.3136 * d
0 = 36 + 0.6272d
-36 = 0.6272d
d = -36 / 0.6272
d ≈ 57.46 m

Therefore, the puck will slide approximately 57 meters before stopping.

The correct answer is D) 57 m.

To determine how far the puck will slide before stopping, we first need to calculate the force of kinetic friction acting on the puck.

The force of kinetic friction can be calculated using the formula:

Friction force = coefficient of kinetic friction * normal force

In this case, the normal force is equal to the weight of the puck, which can be calculated using the equation:

Weight = mass * acceleration due to gravity

Assuming the mass of the puck is not given, we can't directly calculate the weight. However, we can use Newton's second law, which states that force is equal to mass multiplied by acceleration, to find the force.

From Newton's second law, we know that:

Force = mass * acceleration

The force acting on the puck is the net force, which is given by:

Net force = applied force - force of kinetic friction

Since the puck is sliding on a horizontal surface with no other forces acting on it, the applied force is equal to the force of kinetic friction:

Applied force = force of kinetic friction

Therefore, we can write the equation as:

mass * acceleration = coefficient of kinetic friction * mass * acceleration due to gravity

Mass cancels out from both sides of the equation, leaving us with:

acceleration = coefficient of kinetic friction * acceleration due to gravity

Since we're dealing with sliding motion, the acceleration is equal to the deceleration of the puck. Therefore:

deceleration = coefficient of kinetic friction * acceleration due to gravity

To find the deceleration, we use the equation of motion:

final velocity^2 = initial velocity^2 + 2 * acceleration * distance

In this case, the final velocity is 0 since the puck comes to a stop. Plugging in the given values, we have:

0 = (6.0 m/s)^2 + 2 * deceleration * distance

Simplifying this equation, we get:

deceleration * distance = -36.0 m^2/s^2

Since the deceleration is negative (opposite in direction to the initial velocity), we can rewrite this equation as:

-deceleration * distance = 36.0 m^2/s^2

Now we can substitute the expression for deceleration:

-(coefficient of kinetic friction * acceleration due to gravity) * distance = 36.0 m^2/s^2

Rearranging the equation, we find:

distance = -36.0 m^2/s^2 / (coefficient of kinetic friction * acceleration due to gravity)

Plugging in the given values, we get:

distance = -36.0 m^2/s^2 / (0.032 * 9.8 m/s^2)

Calculating this, the negative signs cancel out, and we find:

distance = 112.5 m

Since the distance cannot be negative, we ignore the negative sign and round the result to the nearest whole number. Therefore, the puck will slide approximately 113 meters before stopping.

However, none of the given options match our calculated distance, so it might be a good idea to recheck the calculations or consider rounding off differently.