An Artillery cannon is pointed upwards at an angle 35 degree with the horizontal and fires the projectile with an initial velocity of 200 m/s.If the air resistance is negligible: Find
(a)The maximum height of the projectile
(b)Range of projectile
wikipedia has a nice article on "trajectory" which derives these formulas. You would do well to bookmark it for future reference. Of course, your text probably also has them, so look 'em up.
To find the maximum height of the projectile, we can use the equation for vertical motion. The maximum height occurs when the vertical velocity (Vy) of the projectile becomes zero.
(a) To find the maximum height:
Step 1: Separate the initial velocity into its vertical and horizontal components.
The initial velocity (V) of 200 m/s can be broken down into its vertical component (Vy) and horizontal component (Vx).
Vy = V * sin(θ)
Vx = V * cos(θ)
where θ is the angle of elevation (35 degrees).
Step 2: Calculate the time taken to reach maximum height.
The time taken to reach the maximum height (T) can be determined using the equation for vertical motion:
T = Vy / g
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Step 3: Calculate the maximum height (H).
The maximum height (H) can be found using the equation for vertical motion:
H = (Vy^2) / (2 * g)
Now, let's plug in the values and solve the equations:
Vy = V * sin(θ) = 200 * sin(35)
T = Vy / g = (200 * sin(35)) / 9.8
H = (Vy^2) / (2 * g) = [(200 * sin(35))^2] / (2 * 9.8)
After solving these equations, you will find the maximum height of the projectile.
(b) To find the range of the projectile:
The range of the projectile is the horizontal distance covered by the projectile. It can be calculated using the equation for horizontal motion. The time of flight (Tf), which is the total time it takes for the projectile to return to the same horizontal level, can be found using the equation:
Tf = 2 * T = 2 * [(200 * sin(35)) / 9.8]
The range (R) can be calculated using the equation for horizontal motion:
R = Vx * Tf = (V * cos(θ)) * [(200 * sin(35)) / 9.8]
After solving this equation, you will find the range of the projectile.
Note: In these calculations, we have ignored the effects of air resistance, assuming it to be negligible.