An artillery shell is fired at an angle of 55.7◦ above the horizontal ground with an
initial speed of 1690 m/s. The acceleration of gravity is 9.8 m/s^2.
a.Find the total time of flight of the shell, neglecting air resistance.
Answer in units of min.
b.Find its horizontal range, neglecting air resistance.
Answer in units of km
well for part a we only need to do the vertical problem
Vi = 1690*sin55.7 = 1396 m/s straight up
v = Vi - 9.8 t
v = 0 at top
9.8 t = 1396 at top
t = 142 seconds upward so 2*142.5 in air
t in air = 285 seconds = 4.75 min PART A
u = horizontal speed forever = 1690cos 55.7 = 952 m/s
.952 km/s *285 seconds = 271 km
To find the total time of flight and horizontal range of the artillery shell, we can use the equations of projectile motion. The given information includes the launch angle, initial speed, and acceleration due to gravity.
a. Total time of flight:
The total time of flight can be found by calculating the time it takes for the shell to reach the maximum height and then doubling it.
1. Determine the time to reach maximum height:
We can use the vertical component of the initial velocity and acceleration due to gravity to find the time it takes for the shell to reach its maximum height.
Vertical component of initial velocity (Vy) = initial speed * sin(angle)
Vy = 1690 m/s * sin(55.7°)
Time to reach maximum height (t1) can be found using the equation:
Vy = initial velocity (V0) + acceleration due to gravity (g) * time (t1)
Vy = 0 + (-9.8 m/s^2) * t1
Substitute the value of Vy from the first equation into the second equation and solve for t1.
2. Total time of flight:
Since the time to reach maximum height is equal to the time it takes for the shell to fall back to the ground, we can double the time t1 to find the total time of flight. Multiply by 2.
Convert the total time of flight from seconds to minutes.
b. Horizontal range:
The horizontal range is the distance covered by the shell in the horizontal direction. We can calculate this using the horizontal component of the initial velocity and the total time of flight.
Horizontal component of initial velocity (Vx) = initial speed * cos(angle)
Vx = 1690 m/s * cos(55.7°)
Now, multiply the horizontal component of initial velocity by the total time of flight to find the horizontal range.
Convert the horizontal range from meters to kilometers.
By following the above steps, you can find the total time of flight and horizontal range of the artillery shell.