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AMS 361: Applied Calculus IV by Prof Y. Deng
Homework 5
Assignment Date:
Wednesday (0
3
/11/2009)
Collection Date:
Wednesday (03/18/2009)
Grade:
Each problem is worth 10 points.
Problem 5.1 (Prob. 27, P. 107, Modified)
Suppose that a projectile is fired straight upward from
the surface of the earth with initial velocity
0
2/
vG
M
R
<
. Then its height
y(t)
above the
surface satisfies the initial value problem
2
22
()
dy
GM
dt
y
R
=−
+
,
(0)
0
y
=
,
0
(0)
yv
′
=
. Compute the maximum altitude the projectile
reaches and the time (from launch) for the projectile to reach the maximum altitude.
Problem 5.2 (Prof Deng’s fun problem, modified)
On a straight stretch of road of length
ܮ
there were two stop signs at the two ends. Assume you follow traffic laws: stop at these signs.
Your poor car can accelerate at a constant
ܽ
ଵ
and decelerate at another constant
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