SOLUTION: An object is launched from a platform above the ground, the objects path is modeled with the function h(t) = -4.9t² + 19.6t + 58.8 where h(t) is the height of the object in meters

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: An object is launched from a platform above the ground, the objects path is modeled with the function h(t) = -4.9t² + 19.6t + 58.8 where h(t) is the height of the object in meters      Log On


   

Question 1206277: An object is launched from a platform above the ground, the objects path is modeled with the function h(t) = -4.9t² + 19.6t + 58.8 where h(t) is the height of the object in meters above the ground and t is time in seconds.
1. Use the function to predict the height of the object after one second? [t = 1]
2. Plug the function into Desmos. How many seconds will it take for the object to land? [h(t) = 0]
3. How long does it take for the object to reach its maximum height? How high does it go?
1. h(1) = ____ meters.
2. The object lands after ____ seconds.
3. The max height is ____ meters and it occurs at _____ seconds.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

h%28t%29+=+-4.9t%5E2+%2B+19.6t+%2B+58.8+
1. Use the function to predict the height of the object after one second?
t+=+1
h%281%29+=+-4.9%2A1%5E2+%2B+19.6%2A1+%2B+58.8
h%281%29+=+73.5

2. Plug the function into Desmos. How many seconds will it take for the object to land?
h%28t%29+=+0
-4.9t%5E2+%2B+19.6t+%2B+58.8+=0
https://www.desmos.com/calculator
or
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+80%2C+-4.9x%5E2+%2B+19.6x+%2B+58.8%29+

from the graph we see h%286%29+=+0 and h%28-2%29+=+0 (disregard t=-2, time cannot be negative)
it will take 6+seconds for the object to land

3. How long does it take for the object to reach its maximum height? How high does it go?
find first derivative and equal to zero
h'%28t%29=+-4.9%2A2t+%2B+19.6=-9.8+t%2B+19.6
-9.8+t%2B+19.6=0
19.6=9.8t
t=19.6%2F9.8+
t+=2
it will take 2 sec for the object to reach its maximum heigh
h%282%29+=+-4.9%2A2%5E2+%2B+19.6%2A2+%2B+58.8
h%282%29+=+78.4+meters

2. The object lands after 6 seconds.
3. The max height is 78.4 meters and it occurs at t=2 seconds.