A gun fires a shell at an angle of elevation of 30 degrees with a velocity of 2*10^3m/s. What is the horizontal and vertical component of the velocity? What is the range of the shell? how high will the ball rise

My answer for the range is 346.4

To find the horizontal and vertical components of the velocity, we can use trigonometry.

The horizontal component (Vx) of the velocity can be calculated using the formula:
Vx = V * cos(θ)

Here, V is the magnitude of the velocity and θ is the angle of elevation.

Given that the magnitude of the velocity is 2*10^3 m/s and the angle of elevation is 30 degrees, we can substitute these values into the formula:
Vx = 2*10^3 * cos(30)

Using the scientific calculator, calculate the cosine of 30 degrees which is √3/2, substitute the value:
Vx = 2*10^3 * (√3/2)
Vx ≈ 1.732 * 10^3 m/s

So, the horizontal component of the velocity is approximately 1.732 * 10^3 m/s.

The vertical component (Vy) of the velocity can be calculated using the formula:
Vy = V * sin(θ)

Again, substituting the given values:
Vy = 2*10^3 * sin(30)

Using the scientific calculator, calculate the sine of 30 degrees which is 1/2, substitute the value:
Vy = 2*10^3 * (1/2)
Vy = 10^3 m/s

So, the vertical component of the velocity is 10^3 m/s.

To find the range of the shell, we can use the formula for horizontal range (R):
R = (V^2 * sin(2θ)) / g

Here, V is the magnitude of the velocity, θ is the angle of elevation, and g is the acceleration due to gravity.

Substituting the given values:
R = (2*10^3)^2 * sin(2 * 30) / g
R = (4 * 10^6 * √3/2) / g

Using the standard value for g = 9.8 m/s^2:
R = (4 * 10^6 * √3/2) / 9.8
R ≈ 12,247 m

So, the range of the shell is approximately 12,247 m.

To find how high the shell rises, we can use the formula for vertical displacement (H):
H = (Vy^2) / (2 * g)

Substituting the given values:
H = (10^3)^2 / (2 * g)
H = 10^6 / (2 * 9.8)
H ≈ 51,020 m

So, the ball will rise approximately 51,020 m.

51,020m

Correct and good

the answer is not explanable

horizontal component

Vo = 2000m/s @ 30o.

Xo = 2000*cos30.
Yo = 2000*sin30 = 1000 m/s.

Range = Vo^2*sin(2A)/g.
Vo = 2000 m/s.
2A = 60o.
g = 9.8m/s^2.

hmax = (Y^2-Yo^2)/2g.
hmax = (0-10^6)/19.6 = 51,020 m.