AMERICAN UNIVERSITY IN CAIRO
ENGR 214
Mid Term Exam 1, 12 March, 2008
1. (30) A ball is thrown vertically upward from a point on a tower located 25 meters above the
ground. Knowing that the ball hit the ground 3 seconds after it was released, determine the speed with
which the ball
(a) was thrown upward,
(b) hit the ground,
(c) would hit the ground if it were thrown downward with the same speed obtained in (a).
2. (40) Prove that for a given launch speed v, the
launch angle = 45° yields the maximum horizontal
range R. Determine the maximum range. Neglect air
resistance.
v
3. (30) Determine the proper banking angle
for the
aircraft flying at 600 km/h and making a turn of 3-km
radius. Note that the force exerted by the air is normal to
the supporting wing surfaces.
Useful equations
v=
dx
dt
a=
dv d 2 x
dv
= 2 =v
dt dt
dx
Uniform rectilinear motion: x = x0 + vt
Uniformly accelerated rectilinear motion: v = v0 + at
, x = x0 + v0t + 12 at 2
Acceleration components:
dv
dt
Tangential & normal
at =
Radial and transverse
ar = r r
Other useful relations
sin 2 = 2sin cos
,
2
an =
v2
, a = r + 2r
, v 2 = v02 + 2a ( x x0 )