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3.) A 45-caliber bullet fired straight up from the surface of the moon would reach a height of s =832/ —2.6¢> feet after # seconds. On Earth, in the absence of air, its height would be s =832¢—16¢> feet after 7 seconds. How long would it take the bullet to hit the ground in either case? | Earth Moon I'he bullet hits the ground when s =0 The bullet hits the ground when s =0 832t —161* =0 832t -2.6* =0 -16t(t-52)=0 —-2.6t(t—320)=0 t=52 t=320 The bullet will hit the ground after 52 seconds. The bullet will hit the ground after 320 seconds. 4.) Phineas and Ferb are standing on the top deck of the Eiffel Tower which is 906 feet high. Phineas drops a penny while Ferb throws his penny and it hits the ground in 8 seconds. How long will it take Phineas’s penny to hit the ground and what was the initial velocity of Ferb’s penny? Phineas's Penny Ferb's Penny sp(t)=-16t* +906 5,.(t) ==16t" +v,t +906 Phineas's penny hits the ground Since Ferb's penny hits the ground after 8 seconds, when s, (1)=0 weknow s, (8) =0 -16¢* +906 =0 —16(8)* +v,(8)+906 =0 —-1024+8v,+906=0 8v, =118 v, =14.75 Phineas’s penny hits the ground after 7.525 seconds. ~ Ferb threw his penny with an initial velocity of 14.75 feet per second. 5.) A diveris on a diving board 12 meters above the water. He dives vertically from the board with initial velocity of 4.9 meters/sec. a.) How high will the diver get above the water? b.) How long will it take the diver to hit the water? s(t)=—4.9> +4.9t +12 The diver will hit the water when s(¢) = 0. The diver reaches his maximum —4.9 +4.9t+12=0 height when v(¢) = 0. Using your graphing calculator, s'@)=v(t)=-9.8t+4.9=0 t~-1.143 and 2.143 t=0.5 Therefore, the diver hits the water after His maximum height is 2.143 seconds. 5(0.5) =—4.9(0.5)* +4.9(0.5)+12 =13.225 The diver's maximum height is 13.225 meters above the water. 6.) A helicopter pilot drops a W ground rising at 20 ft/sec.