Answer:
answer
Explanation:
The rocket is 19.5 m above the ground when h=19h=19:
h19.50tttamp;=−8t2+32tamp;=−8t2+32tamp;=−8t2+32t−19.5amp;=−32±322−4(−8)(−19.5)−−−−−−−−−−−−−−−−√2(−8)amp;=−32±1024−624−−−−−−−−−√−16amp;=−32±400−−−√−16amp;=−32±20−16amp;=−32+20−16=0.75amp;=−32−20−16=3.25amp;amp;amp;amp;amp;amp;amp;amp;Substitute h=19.amp;Subtract 19.5 on both sides.amp;Solve for t using the Quadratic Formula.amp;Simplify.amp;Subtract.amp;Evaluate the root.amp;Find the two solutions.
h
19.5
0
t
t
t
amp;=−8t
2
+32t
amp;=−8t
2
+32t
amp;=−8t
2
+32t−19.5
amp;=
2(−8)
−32±
32
2
−4(−8)(−19.5)
amp;=
−16
−32±
1024−624
amp;=
−16
−32±
400
amp;=
−16
−32±20
amp;=
−16
−32+20
=0.75
amp;=
−16
−32−20
=3.25
amp;
amp;
amp;
amp;
amp;
amp;
amp;
amp;Substitute h=19.
amp;Subtract 19.5 on both sides.
amp;Solve for t using the Quadratic Formula.
amp;Simplify.
amp;Subtract.
amp;Evaluate the root.
amp;Find the two solutions.
The rocket will then be at least 19.5 m above the ground for the interval 0.75≤t≤3.25
0.75≤t≤3.25
