An artillery shell is fired at an angle of 86◦
above the horizontal ground with an initial
speed of 1630 m/s.
The acceleration of gravity is 9.8 m/s
2
.
Find the total time of flight of the shell,
neglecting air resistance.
Answer in units of min
Vo = 1630 m/s[86o]
Yo = 1630*sin86 = 1626 m/s.
Y = Yo + g*Tr = = 0 @ max Ht.
Tr = -Yo/g = -1626/-9.8 = 166 s. = 2.77
Min.
Tf = Tr = 2.77 min. = Fall time.
Tr + Tf = 2.77 + 2.77 = 5.54 Min. = Time
in flight.
To find the total time of flight of the shell, we can break down its motion into horizontal and vertical components.
The horizontal component of the initial velocity can be found using the equation:
Vx = V * cos(theta)
where Vx is the horizontal component of the velocity, V is the initial speed of the shell, and theta is the firing angle.
Substituting the given values, we find:
Vx = 1630 m/s * cos(86°)
Vx ≈ 1630 m/s * 0.087
So, Vx ≈ 142.03 m/s
The horizontal motion of the shell is unaffected by gravity, so the time of flight in the horizontal direction (t) can be found using the equation:
t = distance / Vx
where distance is the horizontal distance covered by the shell. However, since the distance is not given, we need to find it using the vertical motion of the shell.
The vertical component of the initial velocity can be found using the equation:
Vy = V * sin(theta)
where Vy is the vertical component of the velocity.
Substituting the given values, we find:
Vy = 1630 m/s * sin(86°)
Vy ≈ 1630 m/s * 0.996
So, Vy ≈ 1623.38 m/s
We can find the time taken for the shell to reach its highest point (t_h) using the equation:
t_h = Vy / g
where g is the acceleration due to gravity.
Substituting the given values, we find:
t_h = 1623.38 m/s / 9.8 m/s^2
t_h ≈ 165.7 s
Since the time of flight is symmetrical, the total time of flight (t_total) is given by:
t_total = 2 * t_h
t_total ≈ 2 * 165.7 s
t_total ≈ 331.4 s
To convert the time to minutes, we divide the time in seconds by 60:
t_total = 331.4 s / 60
t_total ≈ 5.52 min (rounded to 2 decimal places)
Therefore, the total time of flight of the shell, neglecting air resistance, is approximately 5.52 minutes.