A sandbag is released by a balloon that is rising vertically at a speed of 16 feet per second when it reaches a height of 64 feet. (a) How long will it take the bag to hit the ground after it is released? (b) How quickly will it strike the ground?

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Fachur · Accepted Answer

a)  We will use the formula:  s=ut+12at2  The bag will hit the ground when x=-64  Substitute: u=+16, because initial velocity of bag after release is 16ft/s  Substitute: a=-32  −64=16t+12(−32)t2  16t2−16t−64=0  Divide throughout by 16  t2−t−4=0  Using the quadratic formula  t=−(−1)±(−1)2−4(1)(−4)2(1)  t=1±1+162  t=1±172  t must be positive, so we reject the negative solution  t=1+172≈2.562  The bag will hit the ground after 2.562 seconds  b) v=u+at  Substitute: u=16, a=-32 and t=2.562  v=16+(−32)(2.562)=−65.984  The bag will hit the ground with a speed of 65.984 ft/sec

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A balloon, rising vertically with a velocity of 16 feet per second, releases a s

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