Question 20 Suppose that a projectile is fired from a cannon situated at the origin o of an xy -plane, and is inclined at an angle 0 with the horizontal. The initial velocity of the projectile is u ft/s. Assume that there is no air resistance and a flat stationary earth. The dashed curve in the figure represents the path of the projectile. ov represents the muzzle velocity, a vector with magnitude u, and a direction in the xy-plane making an angle e with the x-axis. The components of velocity in the x and y directions are u cose and u sin 8, respectively. Since, there is no air resistance; the only force acting on the projectile of mass m is its weight mg acting vertically downward. Also, the force acting in the x-direction is zero, and a, = and ay = at From the Newton's law, the relations are dx = 0 dt = 0 or and a'y m at = -mg or = -g and Moreover, the initial conditions are x = 0, y = 0, = u cos 0, 2 = u sin 8 att= 0 a) Find the position of the projectile at any time. b) A projectile is fired from a cannon which makes an angle of 60° with the horizontal. If the muzzle velocity is 160 ft/s. Find the time of flights. (Assume g = 32 fts 2.) W=mg A A projectile fired from a cannon from the origin of xy- plane
Question 20 Suppose that a projectile is fired from a cannon situated at the origin o of an xy -plane, and is inclined at an angle 0 with the horizontal. The initial velocity of the projectile is u ft/s. Assume that there is no air resistance and a flat stationary earth. The dashed curve in the figure represents the path of the projectile. ov represents the muzzle velocity, a vector with magnitude u, and a direction in the xy-plane making an angle e with the x-axis. The components of velocity in the x and y directions are u cose and u sin 8, respectively. Since, there is no air resistance; the only force acting on the projectile of mass m is its weight mg acting vertically downward. Also, the force acting in the x-direction is zero, and a, = and ay = at From the Newton's law, the relations are dx = 0 dt = 0 or and a'y m at = -mg or = -g and Moreover, the initial conditions are x = 0, y = 0, = u cos 0, 2 = u sin 8 att= 0 a) Find the position of the projectile at any time. b) A projectile is fired from a cannon which makes an angle of 60° with the horizontal. If the muzzle velocity is 160 ft/s. Find the time of flights. (Assume g = 32 fts 2.) W=mg A A projectile fired from a cannon from the origin of xy- plane
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 20
Suppose that a projectile is fired from a cannon situated at the origin o of an xy-plane, and is inclined at an angle 0 with the
horizontal. The initial velocity of the projectile is u ft/s. Assume that there is no air resistance and a flat stationary earth. The
dashed curve in the figure represents the path of the projectile. OV represents the muzzle velocity, a vector with magnitude
u, and a direction in the xy-plane making an angle e with the x-axis. The components of velocity in the x and y directions
are u cos e and u sin 8, respectively. Since, there is no air resistance; the only force acting on the projectile of mass m is its
weight mg acting vertically downward. Also, the force acting in the x-direction is zero, and
ax =
and
ay =
at?
From the Newton's law, the relations are
= 0
d²x
%3D
m
dt2
or
dt
and
= -mg
a'y
= -g
m
at
or
and
Moreover, the initial conditions are
dy
x = 0,
y = 0,
= u cos 0, 2
= u sin e att = 0
a) Find the position of the projectile at any time.
b) A projectile is fired from a cannon which makes an angle of 60° with the horizontal. If the muzzle velocity is 160 ft/s.
Find the time of flights. (Assume g 32 fts 2.)
W=mg
A projectile fired from a cannon from the origin of xy-plane
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