A young girl standing on a bridge throws a stone with an initial velocity of \(12 \mathrm{~m} / \mathrm{s}\) at a downward angle of \(45^{\circ}\) to the horizontal, in an attempt to hit a block of wood floating in the river below (Figure 3.14). If the stone is thrown from a height of \(20 \mathrm{~m}\) and it just reaches the water when the block is \(13 \mathrm{~m}\) from the bridge, does the stone hit the block? (Assume that the block does not move appreciably and that it is in the plane of the throw.)

THINKING IT THROUGH. The question is, what is the range of the stone? If this range is the same as the distance between the block and the bridge, then the stone hits the block. To find the range of the stone, we need to find the time of descent (from the \(y\)-component of motion) and then use this time to find the distance \(x_{\max }\). (Time is the connecting factor.)

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x = 0, yo 0 (launch point) 45 y=-20 m block = 13 m FIGURE 3.14 A throw from the bridge Hit or miss? See Example 3.7 for description.