AE/ME 2360 Dynamics Fall 2025
Homework One
Due: 11:59 PM, Thursday, September 04
Work the problems symbolically. If the problem provides
numerical values for the parameters, assign them symbols. After
you derive the final answer, plug in the numerical values. Box
both the symbolic and numerical answers
Exercise 1:
The boat travels in a straight line with the acceleration described by the a-s
graph. If it starts from rest, construct the v-s graph and determine the boat’s
maximum speed. What distance s′ does it travel before it stops? When the
boat has travelled s′ distance, how much time has passed since the start?
1
Exercise 2:
Measurements of a shot recorded on a video tape during a basketball game
are shown. The ball passed through the hoop even though it barely cleared
the hands of the player B who attempted to block it. Neglecting the size of
the ball, determine the magnitude vA of its initial velocity and the height h
of the ball when it passes over player B. Also, compute the velocity of the
ball as it passes over player B. Give all answers in SI units.
2
Exercise 3:
At the same instant two boys throw balls A and B from the window with a
speed v0 and kv0 , respectively, where k is a constant. Show that the balls
cos θ2
.
will collide if k = cos
θ1
Now, if the gravity of the Earth suddenly vanishes, find the condition on
k such that the balls will collide.
3
Exercise 4:
The balloon A is ascending at the rate vA = 12 km/h and is being carried
horizontally by the wind at vw = 20 km/h.
(a) If a ballast bag is dropped from the balloon such that it takes 20 s for
it to reach the ground, determine the balloon’s altitude h at the instant the
bag was released.
(b) If a ballast bag is dropped from the balloon at altitude h = 100 m,
determine the time needed for it to strike the ground. Also, at what speed
does the bag strike the ground?
(c) How will the answers for parts (a) and (b) change if the balloon A is
ascending at the same rate (12 km/h) but instead of moving horizontally to
the left at 20 km/h, it is now moving horizontally to the right at 20 km/h?
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