The question is asking for the minimum radius of curvature the road must have for safe driving of the van. This is a physics problem involving circular motion and friction.

The force of friction (f) provides the necessary centripetal force for the van to move in a circle. The force of friction can be calculated using the equation f = μN, where μ is the coefficient of friction and N is the normal force. In this case, the normal force is equal to the weight of the van, which is mass (m) times gravity (g).

So, f = μmg.

The centripetal force needed to keep an object moving in a circle is given by the equation F = mv²/r, where m is the mass of the object, v is its speed, and r is the radius of the circle.

So, mv²/r = μmg.

We can cancel out the mass (m) from both sides of the equation, and we're left with:

v²/r = μg.

We're solving for r, so let's rearrange the equation to get r on one side:

r = v²/μg.

We're given that the speed of the van (v) is 72 km/h, which we need to convert to m/s by multiplying by 1000 (to convert km to m) and dividing by 3600 (to convert hours to seconds). So, v = 72 * 1000 / 3600 = 20 m/s.

We're also given that the coefficient of friction (μ) is 0.5 and that gravity (g) is 10 m/s².

Substituting these values into the equation gives us:

r = 20² / (0.5 * 10) = 400 / 5 = 80 m.

So, the minimum radius of curvature the road must have for safe driving of the van is 80 m, which corresponds to option A.

Question

The question is asking for the minimum radius of curvature the road must have for safe driving of the van. This is a physics problem involving circular motion and friction.

The force of friction (f) provides the necessary centripetal force for the van to move in a circle. The force of friction can be calculated using the equation f = μN, where μ is the coefficient of friction and N is the normal force. In this case, the normal force is equal to the weight of the van, which is mass (m) times gravity (g).

So, f = μmg.

The centripetal force needed to keep an object moving in a circle is given by the equation F = mv²/r, where m is the mass of the object, v is its speed, and r is the radius of the circle.

So, mv²/r = μmg.

We can cancel out the mass (m) from both sides of the equation, and we're left with:

v²/r = μg.

We're solving for r, so let's rearrange the equation to get r on one side:

r = v²/μg.

We're given that the speed of the van (v) is 72 km/h, which we need to convert to m/s by multiplying by 1000 (to convert km to m) and dividing by 3600 (to convert hours to seconds). So, v = 72 * 1000 / 3600 = 20 m/s.

We're also given that the coefficient of friction (μ) is 0.5 and that gravity (g) is 10 m/s².

Substituting these values into the equation gives us:

r = 20² / (0.5 * 10) = 400 / 5 = 80 m.

So, the minimum radius of curvature the road must have for safe driving of the van is 80 m, which corresponds to option A.

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