A cannon fires projectile (ordinarily called a cannonball) at an angle 85 degrees from the ground. The cannonball has a speed 150 m/s, and it is launched from hill 20 m above the plain where it will land.
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To find the range and time of flight of the cannonball, we need to use the equations of projectile motion.
Given:
- Angle of launch (θ) = 85 degrees
- Initial speed (v₀) = 150 m/s
- Height of the hill (h) = 20 m
1. Break down the initial velocity into its horizontal and vertical components:
The horizontal component of the initial velocity will remain constant throughout the motion. The vertical component will change due to the effect of gravity.
The horizontal component (v₀x) can be found using the equation:
v₀x = v₀ * cos(θ)
The vertical component (v₀y) can be found using the equation:
v₀y = v₀ * sin(θ)
2. Calculate the time of flight (t):
The time it takes for the projectile to reach the ground can be calculated using the vertical component of velocity.
The time of flight can be found using the equation:
t = (2 * v₀y) / g
where g is the acceleration due to gravity (approximately 9.8 m/s²).
3. Calculate the range (R):
The horizontal distance covered by the projectile can be calculated using the horizontal component of the velocity and the time of flight.
The range can be found using the equation:
R = v₀x * t
4. Correct the range for the initial height (h):
Since the cannonball is launched from a hill, we need to consider its initial height when calculating the range. The actual range is the horizontal distance plus the initial height.
The corrected range can be found using the equation:
R_corrected = R + h
Now, let's plug in the values:
v₀x = 150 m/s * cos(85°)
v₀y = 150 m/s * sin(85°)
t = (2 * v₀y) / g
R = v₀x * t
R_corrected = R + h
After substituting the values and completing the calculations, you will find the range and time of flight of the cannonball.