Question

Alyas tosses two different toy boats into the bath tub. One boat is made out of wood and the other boat is made out of plastic. Both boats go under water before rising back up to float on the surface of the water.The height of the wooden boat, w(t), in inches, at t seconds after being released, can be modeled by the graph shown below for time 0 ≤ t ≤ 5. (Please answer the two questions in the photo)

Answer 1

Part A

Since t-axis represents the surface of the water, the wooden boat reaches the water when w(t) = 0, and the plastic boat reaches the water when p(t) = 0.

Thus, the time tw for which the wooden boat reaches the water is found in the graph. That corresponds to the first time when w(t)=0. So, tw = 1.

Now, for the plastic boat, we need to find in the table the value of t for which p(t) = 0. That happens in tp = 3.

Since tw < tp, the wooden boat reaches the water first.

Part B

The more negative the height becomes, the deeper the respective boat is under the water.

From the graph, we see that the most negative value for w(t) is -8.

And, from the table, we see that the most negative value for p(t) is -1.

Since -8 is more negative than -1, the wooden boat goes deeper into the bath tube.