G -v Math 1910: Section 4. X(3) optimization YouTube e Calculus question Chegg o
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G -v Math 1910: Section 4. X(3) optimization YouTube e Calculus question Chegg optimization problems wit webassign net/web Student/Assignment-Responses submit?dep-17481336 Chargernet Online Campus V WebAssign ** Week at a GlanceMicrosoft Office [Sr] Student Travel Habitica Tasks Math way Math Problem : + v LTX 11. -4 points SCalcET8 4.9.065. 0/6 Submissions Used My NotsAsk Your Teacher A stone is dropped from the upper observation deck of a tower, 500 m above the ground. (Assume g = 9.8 m/s (a) Find the distance (in meters) of the stone above ground level at time t h(t) = (b) How long does it take the stone to reach the ground? (Round your answer to two decimal places.) (c) With what velocity does it strike the ground? (Round your answer to one decimal place.) m/s (d) If the stone is thrown downward with a speed of 4 m/s, how long does it take to reach the ground? (Round your answer to two decimal places.) Need Help? Read It Watch It Talk to a Tutor Submit Answer Save 9:53 PM Type here to search 11/16/20172Explanation / Answer
Acceleration due to gravity is -9.81 m/s².
Integration of acceleration w.r.t. time gives you velocity:
-9.81 dt = -9.81t + C
= C - 9.81t
C is the starting velocity, which we will call v. Velocity is:
v(t) = v - 9.81t
Integration of velocity w.r.t. time gives you height:
v - 9.81t dt = vt - 4.905t² + C
= C + vt - 4.905t²
Now the constant C is the starting height, 500 m. Height is:
h(t) = 500 + vt - 4.905t²
Assuming the stone is dropped (v = 0 m/s),
(a) distance above ground level is
h(t) = 500 - 4.905t²
(b) solve h(t) = 0:
500 - 4.905t² = 0
4.905t² = 500
t = (500/4.905) 10.096 sec
(c) solve v(t) for t = (500/4.905)
-9.81(450/4.905) --99.0454 m/s
(d) set v = - 4 m/s, and solve h(t) = 0 again. This time it takes a little more work to solve the quadratic, since there is a starting velocity. You could use the quadratic equation, but I will complete the square:
500 - 4t - 4.905t² = 0
t² + (4/4.905)t = 500/4.905
t² + (4/4.905)t + (4/9.81)² = 500/4.905 + (4/9.81)²
(t + 4/9.81)² = 500/4.905 + 16/96.2361
t + 4/9.81 = ±(500/4.905 + 16/96.2361)
t = -4/9.81 ± (500/4.905 + 16/96.2361)
Test both for the ±:
t = -4/9.81 - (500/4.905 + 16/96.2361) -10.51235 sec
…this is a negative number. We only care about t > 0. So, not a solution.
t = -5/9.81 + (450/4.905 + 25/96.2361) 9.69686 sec
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