A tightrope walker wonders if her rope is safe. Her mass is 60 kg and the length of the rope is about 20 m. The rope will break if its tension exceeds 7500 N.

What is the smallest angle at which the rope can bend up from the horizontal on either side of her to avoid breaking?
Express your answer to two significant figures and include the appropriate units.

To determine the smallest angle at which the rope can bend up from the horizontal on either side of the tightrope walker, we need to consider the tension in the rope.

The tension in the rope can be found using the formula:

Tension = mass * acceleration

In this case, the acceleration can be approximated as the acceleration due to gravity (9.8 m/s^2).

Tension = mass * acceleration
Tension = 60 kg * 9.8 m/s^2
Tension = 588 N

The tension in the rope should not exceed 7500 N to avoid breaking.

To find the smallest angle at which the rope can bend up from the horizontal, we need to consider the vertical component of the tension. This can be calculated using the equation:

Vertical Component of Tension = Tension * sin(angle)

Rearranging the equation to solve for the angle, we get:

angle = arcsin(Vertical Component of Tension / Tension)

Substituting the values into the equation:

angle = arcsin(7500 N / 588 N)

Using a calculator, we find:

angle ≈ 86.58°

Therefore, the smallest angle at which the rope can bend up from the horizontal on either side of the tightrope walker is approximately 86.58°.