The advertisement for a new shoe promises runners less slip. The coefficient of friction (μ) between concrete and a new material used in the sole of this shoe is 1.5. The force of friction that causes slip is equal to mg sinθ, where m is a runner’s mass and g is the acceleration due to gravity. The force that prevents slip is μmg cosθ.

Write an equation to find the angle at which a shoe with a coefficient of friction of 1.3 will slip.

At what angle will this shoe start to slip?

52.4 deg
57 deg
66.2 deg
77 deg

Suggest how the new shoes might improve Mukisa's performance.

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To find the angle at which a shoe with a coefficient of friction of 1.3 will slip, we can set the force of friction that causes slip (mg sinθ) equal to the force that prevents slip (μmg cosθ). Plugging in the given coefficient of friction (μ = 1.3), we get the equation:

mg sinθ = μmg cosθ

Simplifying the equation by canceling out the mass (m) terms, we have:

sinθ = μ cosθ

To solve for θ, we can take the inverse sine of both sides:

θ = sin^(-1)(μ cosθ)

Now we can substitute the value of μ into the equation to find the angle at which the shoe will slip:

θ = sin^(-1)(1.3 cosθ)

Unfortunately, we cannot determine the exact angle without having the numerical value of cosθ. However, we can make some suggestions based on the given answer choices.

Given the answer choices of 52.4 deg, 57 deg, 66.2 deg, and 77 deg, we can test each angle by calculating the left side (sinθ) and right side (μ cosθ) of the equation and see if they are approximately equal.

For example, if we test θ = 52.4 deg:
sin(52.4) ≈ 0.793
1.3 cos(52.4) ≈ 0.847

Since these values are not equal, we can conclude that 52.4 deg is not the angle at which the shoe will slip. We can repeat this process for the other answer choices and see which one gives us an approximate equality between the left and right sides of the equation.

Regarding how the new shoes might improve Mukisa's performance, we can see from the given information that the coefficient of friction between the new material used in the sole and concrete is 1.5, which is greater than the coefficient of friction of the older shoe (1.3). A higher coefficient of friction means that the shoe can provide a stronger force of friction, which will improve traction and reduce slipping. This can result in better performance for Mukisa as they will have more stability and control while running.