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14 Dec 2020, 04:00
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A model rocket is shot straight up in the air from ground level. After 2 seconds and then again after 3 seconds, its height is 96 feet. Which of the following equations could define rocket’s height, (h), as a function of the number of seconds after launch (t)?
(A) h = 10t^2 – 74t
(B) h = 8t^2 – 64t
(C) h = 64t – 8t^2
(D) h = 80t – 16t^2
(E) h = 96t – 10t^2
(A) h = 10t^2 – 74t
(B) h = 8t^2 – 64t
(C) h = 64t – 8t^2
(D) h = 80t – 16t^2
(E) h = 96t – 10t^2
14 Dec 2020, 09:14
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Here the rocket reaches at 96 ft after 2 sec during upward motion & again reaches at 96 ft during downward motion after 3 sec. So the rocket reaches its maximum height from the ground between 2 and 3 sec.
One can put t=2 & t=3 in all the equations to find the right equation which provides 96 ft in both cases. Option D satisfies the condition.
One can put t=2 & t=3 in all the equations to find the right equation which provides 96 ft in both cases. Option D satisfies the condition.
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14 Dec 2020, 09:33
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After 2 seconds and then again after 3 seconds, the height is 96 feet.
that means H will be 96, irrespective of T being 2 or 3
Putting T = 3 and H = 96
(A) h = 10t^2 – 74t
96 = 10(3)^2 – 74(3)
96 = 10*9-222
96 is not equal to -132
(B) h = 8t^2 – 64t
96 = 8(3)^2 – 64(3)
96 = 8*9-192
96 is not equal to -120
(C) h = 64t – 8t^2
96 = 64(3)-8(3)^2
96 = 192-72
96 is not equal to 120
(D) h = 80t – 16t^2
96 = 80(3)-16(3)^2
96 = 240-144
96 = 96
try for t = 2
96 = 80(2)-16(2)^2
96 = 160-64
96 = 96
(answer)
(E) h = 96t – 10t^2
96 = 96(3)-10(3)^2
96 = 288-90
96 is not equal to 198
Answer is D
that means H will be 96, irrespective of T being 2 or 3
Putting T = 3 and H = 96
(A) h = 10t^2 – 74t
96 = 10(3)^2 – 74(3)
96 = 10*9-222
96 is not equal to -132
(B) h = 8t^2 – 64t
96 = 8(3)^2 – 64(3)
96 = 8*9-192
96 is not equal to -120
(C) h = 64t – 8t^2
96 = 64(3)-8(3)^2
96 = 192-72
96 is not equal to 120
(D) h = 80t – 16t^2
96 = 80(3)-16(3)^2
96 = 240-144
96 = 96
try for t = 2
96 = 80(2)-16(2)^2
96 = 160-64
96 = 96
(answer)
(E) h = 96t – 10t^2
96 = 96(3)-10(3)^2
96 = 288-90
96 is not equal to 198
Answer is D
