A ball is dropped onto a step at point A and rebounds with a velocity vo at an angle of 15° with the vertical. Determine the value of vo knowing that just before the ball bounces at point B its velocity vB forms an angle of 12° with the vertical. Also determine the velocity of B, vB and the distance d.

v₀ = 2.68 m/s.

= 3.33 m/s

d = 1.61 m

Explanation:

Searching on the internet I found the picture of the answer in which the height between point A and point B is equal to 0.2 m.

To determine the value of v₀ we need to use the following equation:

Taking the initial vertical velocity () as and the final vertical velocity () as we have:

We can express the time (t) in terms of the velocities of A and B:

   (1)

Now, we can use the equation:

  (2)

By entering equation (1) into equation (2):

     (3)

Since because there is no acceleration in the horizontal movement, we have:

   (4)

Taking:

= 0

= 0.2 m

g = 9.81 m/s²

Entering the above values and equation (4) into equation (3) we have:

By solving the above quadratic equation:

Hence, the velocity of the ball is 3.33 m/s.

Now, we can find by using equation (4):

Then, the value of v₀ of the ball is 2.68 m/s.

Finally, to find the distance between point A and point B we need to calculate the time by using equation (1):

The minus sign in is because the vertical component of the vector is negative.

Now, the distance is:

I hope it helps you!            

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