A model rocket is shot straight up in the air from ground level. After

Question

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

Rahul Biswas · Answer

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.

yashikaaggarwal · Answer

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

CrackverbalGMAT · Answer

Since t = 2 ans t = 3 satisfies the equation formed, then (t - 2)(t - 3) = 0

therefore  t^2 - 5t + 6 = 0

Since the height reach is 96 feet, it will be a multiple of 6 = 16 * 6

Therefore  16t^2 - 80t + 96 = 0

or 96 = h =  80t - 16t^2

Option D

Arun Kumar

KarishmaB · Answer

It takes 2 secs to reach height of 96 and then the rocket reaches the maximum height and falls back and at 3 secs, it is again at 96 feet. In another 2 secs i.e. total 5 secs after starting, it will touch the ground again.

The options give us the relation between t and h. We already know that when t = 2, h = 96, when t = 3, h = 96 and when t = 5, h = 0.

Put t = 2 in the options. 
Option (A) first term is smaller than 74 - Eliminate
Option (B) first term is smaller than 64 - Eliminate
Option (C) if t = 2, 8t(8 - 2) = 96. Put t = 3, 8t(8 - 3) = 120 - Eliminate
Option (D) if t = 2, 16t(5 - 2) = 96. Put t = 3, 16t(5 - 3) = 96. Answer
Option (E) 96t is much greater than 40 - Eliminate

Answer (D)

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A model rocket is shot straight up in the air from ground level. After

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