Calculate the horizontal projectile range with the cannon elevated 6m above the x-axis, with an initial speed of 14 m/s and an initial launch angle of 14 degrees.

The horizontal projectile range is 20.44m

Explanation:

To determine the range of the projectile we need to first determine the total time of flight.

Using the vertical component of the motion.

The first phase of flight (moving up)

Using equation of motion.

h = ut + 0.5at^2 + h0 ... 1

a = - g (acceleration due to gravity acting against motion) = - 9.8m/s^2

u = vertical initial speed = 14sin14°

h0 = initial height = 6m

h = 0 (on the x axis y = 0)

Equation 1, becomes;

h = ut - 0.5gt^2 + h0

Substituting the values

0 = 14sin14 (t) - 4.9t^2 + 6

3.39t - 4.9t^2 + 6 = 0

Solving the quadratic equation, we have;

t = 1.505s or t = - 0.814s

time cannot be negative, so

t = 1.505s

Since the total time of flight is 1.505s

The range R = Vx * t

Vx = horizontal speed = 14cos14 m/s

R = 14cos14 * 1.505

Range R = 20.44 m

d = 20.25 m

Explanation:

h = 6m, V = 14 m/s, θ=14°

⇒ Vx=V * Cosθ=13.58 m/s and Vy = V * Sinθ=3.39 m/s

to find time t by h=-Vy t + 1/2 g t² (after putting value and simplifying) (-ve for downward motion)

4.9 t² - 3.39 t - 6 = 0

⇒ t=1.5 sec (ignoring - ve root)

Now Vx = d/t

13.5 m/s = d / 1.5 s ⇒ d = 20.25 m