Question

A basketball rolls off a deck that is 3.2 m from the pavement. The basketball lands 0.75 m from the edge of the deck. How fast was the basketball rolling? Seema lists the given values in a chart and determines that the unknown value is vx.

given: value:
change in y 3.2m
ay -9.8 m/s2
change in x 0.75m

Which describes Seema’s error?

A. The y and x values are switched.
B. The unknown is , not vx.
C. The value for ay is not known.
D. The value of y should be –3.2 m.

Answer 1

D. The value of y should be –3.2 m.

Step-by-step explanation:

We have to remember that when we are talking about free fall, or parabolic motion, we have two types of Y distance, positive and negative, positive for when the object is going up, and negative for when the object is going down, since the ball goes from 3.2m at the deck, to the ground those are -3.2 meters since the ball is loosing altitude. So Seema´s error is setting Change in Y as positive.

Answer 2

The table is almost perfect. BUT ... since she called ay negative, that means she's calling the upward direction positive-y and the downward direction negative-y. In that case, since the ball moves downward from the deck to the pavement, the change in y should be negative 3.2 m. Everything else in her table is fine. Choice-D is the good one.

Now, regarding the speed of the ball ...
How long does it take to fall 3.2 m ?
Use the formula. D = 1/2 g T^2 .

3.2 = 4.9 T^2.

T^2 = 3.2/4.9

T = √(3.2/4.9) = 0.808 second.

The ball hit the pavement 0.808 second after it rolled off the deck. So that's also the time it took to move the 0.75 m horizontally.

Speed = distance / time

Speed = 0.75 m / 0.808 second

Speed = 0.928 meter/second .