A basketball player is shooting a basketball toward the net. The height, in feet, of the ball t seconds after the shot is modeled by the equation h = 6 + 30t – 16t2. Two-tenths of a second after the shot is launched, an opposing player leaps up to block the shot. The height of the shot blocker’s outstretched hands t seconds after he leaps is modeled by the equation h = 9 + 25t – 16t2. If the ball was on a path to reach the net 1.7 seconds after the shooter launches it, does the leaping player block the shot?
A
yes, exactly 0.6 seconds after the shot is launchedB
yes, between 0.64 seconds and 0.65 seconds after the shot is launchedC
yes, between 0.84 seconds and 0.85 seconds after the shot is launchedLet T be the time since the shot was launched. At time T, the blocker has been leaping for T − 0.2 seconds. Substituting that into the blocker’s equation gives a height of 3.36 + 31.4T − 16T² feet, while the ball’s height is 6 + 30T − 16T² feet. The ball stays above the blocker until their heights would meet at T = 2.64 ÷ 1.4 ≈ 1.89 seconds, which is after it reaches the net at 1.7 seconds; therefore, the shot is not blocked.
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