A gun fires a shell at an angle of elevation of 30 degree with a velocity of 2×10m what are the horizontally and vertical components of the velocity? What is the range of the shell?how high will it rise
Please i want the ans
initial velocity up = Vi = whatever you typed * sin 30
sin 30 = 1/2
horizontal velocity forever = u = same whatever * cos 30 = 0.866 * whatever
for height
(1/2) m Vi^2 = m g h
h = Vi^2 / 2g
how long in the air?
v = Vi - g t
v = 0 at top
so t = Vi/g at top
has to fall then so time in air = 2 Vi/g
then range = u * 2 Vi/g
To find the horizontal and vertical components of the velocity, we can use trigonometry.
The horizontal component (Vx) is given by V * cos(θ), where V is the velocity and θ is the angle of elevation.
Vx = 2 × 10 m/s * cos(30°)
Vx ≈ 2 × 10 m/s * 0.866
Vx ≈ 17.32 m/s
The vertical component (Vy) is given by V * sin(θ).
Vy = 2 × 10 m/s * sin(30°)
Vy ≈ 2 × 10 m/s * 0.5
Vy ≈ 10 m/s
To calculate the range of the shell, we can use the horizontal component of the velocity and the equation of motion for horizontal motion:
Range (R) = Vx * time of flight (t),
where time of flight is the time the shell spends in the air.
To find the time of flight, we can use the equation of motion for vertical motion:
Vertical displacement = Vy * time - 0.5 * g * time^2,
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
At the highest point of the trajectory, the vertical displacement is zero since the shell reaches its maximum height and then falls back down. Therefore, we can calculate the time of flight as follows:
0 = Vy * t - 0.5 * g * t^2
0 = 10 * t - 0.5 * 9.8 * t^2
0 = 10t - 4.9t^2
By solving this quadratic equation, we find that t ≈ 2.04 seconds (rounded to two decimal places).
Now we can calculate the range:
R = 17.32 m/s * 2.04 s
R ≈ 35.34 meters
To calculate the maximum height the shell will reach, we can substitute the time of flight into the equation for vertical motion:
Vertical displacement = Vy * time - 0.5 * g * time^2
h = Vy * t - 0.5 * g * t^2
h = 10 * 2.04 - 0.5 * 9.8 * 2.04^2
h ≈ 20.4 - 0.5 * 9.8 * 4.1616
h ≈ 20.4 - 20.37
h ≈ 0.03 meters
Therefore, the shell will rise to a maximum height of approximately 0.03 meters.