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0593_C08_fm Page 273 Monday, May 6, 2002 2:45 PM

Principles of Dynamics: Newton’s Laws and d’Alembert’s Principle 273

P8.5.2: Repeat Problem P8.5.1 for a tube radius r of 0.5 m, a particle mass m of 0.1 kg, and
a speed v relative to the tube of 1 m/sec.
P8.5.3: Repeat Problems P8.5.1 and P8.5.2 if the rotation rate Ω of the tube is increasing
2
2
at 7 rad/sec and the speed v of P relative to the tube is increasing at 10 ft/sec for P8.5.1
2
and 3 m/sec for P8.5.2.
Section 8.7 Projectile Motion
P8.7.1: An object P is thrown vertically from the ground with a speed v . Using Eq. (8.7.11)
0
2
show that the maximum height h reached by P is v 2.
g
0
P8.7.2: See Problem P8.7.1. An object P is dropped from rest at a height h above the ground.
Show that the speed v at which P strikes the ground is 2 gh.
P8.7.3: See Problem P8.7.1. An object P is thrown vertically from the ground with a speed
of 15 ft/sec. Find the maximum height h reached by P.
P8.7.4: See Problem P8.7.2. An object P is dropped from rest from a height of 30 m. Find
the speed of impact of P with the ground.
P8.7.5: A projectile is launched from a horizontal surface at a speed v of 50 ft/sec at an
angle θ of 30° relative to the horizontal as in Figure P8.7.5. Determine the range d where
the projectile impacts the horizontal surface and the maximum height h reached by the
projectile.

v = 50 ft/sec
d
θ = 30° h
FIGURE P8.7.5
A projectile launched on a horizontal plane.

P8.7.6: See Problem P8.7.5. Repeat Problem P8.7.5 for launch angles θ of (a) 35°, (b) 40°,
(c) 45°, (d) 50°, (e) 55°, and (f) 60°. Tabulate and graph the results for d and h as a function
of θ. Verify that the range d is a maximum for θ = 45°.
P8.7.7: See Problem P8.7.5. Repeat Problem P8.7.5 if the projectile is launched from a point
8 ft above the horizontal surface as in Figure P8.7.7.

T
v = 80 ft/sec
v = 50 ft/sec
θ = 30°
h
8 ft
θ
d P

FIGURE P8.7.8
FIGURE P8.7.7 A projectile P launched toward a target T.
A projectile launched above a horizontal surface.

P8.7.8: A projectile P is launched at 80 ft/sec toward a target T which is 30 ft high and 40
ft away (measured horizontally) as in Figure P8.7.8. Determine the appropriate launch
angles θ.