Problem

(Ill) Revisit Example 3-7, and assume that the boy with the slingshot is be few the boy in the tree (Fig. 3-40) and so aims upward, directly at the boy in the tree. Show that again the boy in the tree makes the wrong move by letting go at the moment the water balloon is shot.

FIGURE 3 40 Problem 36

CONCEPTUAL EXAMPLE 3-7 The wrong strategy A boy on a small hill aims hb water-balloon slingshot hwt/untally. straight at a second boy hanging from a tree branch » distance rf away, Bg 3-24 Al the instant the water balloon is released the second boy lets go and fails from the tree, hoping to avoid being hit. Show that he made the wrong move (He hadn't studied physics yet.) Ignore air resistance

RESPONSE Both the water balloon and the boy in the tree start falling at the same instant, and in a time t, both of them fall by the same vertical distance. Thus at every instant, the balloon will have the same vertical position as the falling boy. Splat. If the boy had stayed in the tree, he would have avoided the humiliation.

Problem 34P

Step-by-step solution

Step 1 of 5</p>

The free body trajectories of the balloon and the hanging boy are shown below.

Step 2 of 5</p>

We use the coordinate system shown in the above diagram to see if the water balloon hits the boy. We will find the location of the water balloon and the boy when the water balloon passes the vertical line that the boy follows

We find the time at which this occurs from the horizontal motion of the water balloon

which gives

Step 3 of 5</p>

At this time the location of the boy is