A toy rocket (not internally powered) is launched straight up from the top of a building 50 ft tall at an initial velocity of 200 ft per sec. a) Give the function that describes the height of the rocket in terms of time t. b) Determine the time at which the rocket reaches its maximum height and the maximum height in feet. c) For what time interval will be rocket be more than 300 ft above ground level? d) After how many seconds will it hit the ground?

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A toy rocket (not internally powered) is launched straight up from the top of a building 50 ft tall at an initial velocity of 200 ft per sec.  a) Give the function that describes the height of the rocket in terms of time t.  b) Determine the time at which the rocket reaches its maximum height and the maximum height in feet.  c) For what time interval will be rocket be more than 300 ft above ground level?  d) After how many seconds will it hit the ground?

Arham Warner · Accepted Answer

Step 1The first three questions receive standard responses. to investigate how the thing moves under the current circumstancesStep 2Let H(t) represent the height of the object above the ground. H(t) is calculated using the common equations of motion (under gravity), as indicated. Recall that at&amp;nbsp;t=0, the height is 50 (as given)a)&amp;nbsp;H(t)=ut+0.5at2+50=200t−16t2+50Step 3b) filling in the square to determine the highest point (the same outcome may be attained by settingtting&amp;nbsp;H′(t)=200−32t=0)b) WriteH(t)=200t−16t2+50=50−16(t−6.25)2+16×6.252=675−16(t−6.25)2So,&amp;nbsp;H(t)=maximum at t=6.25sec⁡&amp;nbsp;Step 4c) a height above the earth of at least 300 feet throughout the period between 1.41 and 11.1 secondsc) NecessaryH(t)=200t−16t2+50≥300solve&amp;nbsp;200t−16t2+50=30016t2−200t+250=0t≈1.41,11.1&amp;nbsp;So,height&amp;nbsp;H(t)≥300&amp;nbsp;between 1.41 and 11.1 sec

A toy rocket (not internally powered) is launched straight up from the top of a

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