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A regulation basketball has a 46 cm diameter and may be approximated as a thin spherical shell. How long will it take a basketball starting from rest to roll without slipping 4.4m down an incline that makes an angle of 15.4° with the horizontal?

The acceleration of gravity is 9.81m/s^2? Answer in units of s

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Answer: 2.2 seconds!

Step-by-step explanation:

The answer is approximately 2.2 seconds.

To find this, we can apply the equations of motion for a rolling sphere on an incline. Since the ball is starting from rest, its initial velocity is 0 m/s. We also know the angle of inclination (15.4°) and the distance the ball must travel (4.4m).

Using the equations of motion, we can solve for the acceleration of the ball, which is given by:

a = g*sin(θ)

where g is the acceleration due to gravity (9.81 m/s2) and θ is the angle of inclination (15.4°).

So, the acceleration of the ball is:

a = 9.81 * sin(15.4°) = 3.15 m/s2

Now we can use the equations of motion to solve for the time it will take for the ball to travel the 4.4m.

The equation for displacement is given by:

x = 1/2 * a * t^2

Where x is the displacement (4.4m in this case), a is the acceleration (3.15 m/s2) and t is the time.

Rearranging the equation to solve for t, we get:

t = sqrt(2x/a)

Substituting in the values for x and a, we get:

t = sqrt(2*4.4/3.15) = 2.2 s

Therefore, it will take the basketball approximately 2.2 seconds to roll 4.4m down the incline.

User Henry Barker
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