a cannon fires a shell with a speed of 84m/s.when the cannon is inclined at 45 degree,the horizontal distance covered is observed as 630 m.what is the percentage decrease in the horizontal distance observed due to air resistance?
To find the percentage decrease in the horizontal distance observed due to air resistance, we need to compare the horizontal distance without air resistance to the observed horizontal distance with air resistance.
Let's first calculate the horizontal distance covered without air resistance by considering the projectile motion of the cannon shell.
Since the cannon is inclined at an angle of 45 degrees, we can break down the initial velocity provided as follows:
Horizontal component of velocity (Vx) = Initial velocity * cos(angle)
Vertical component of velocity (Vy) = Initial velocity * sin(angle)
Given:
Initial velocity (V) = 84 m/s
Angle (θ) = 45 degrees
Calculating the horizontal component of velocity:
Vx = 84 * cos(45)
Vx ≈ 84 * 0.707
Vx ≈ 59.39 m/s
To determine the time of flight, we need to consider the vertical motion of the cannon shell. The time taken for the shell to reach its highest point will be the time of flight divided by 2.
Using the formula:
time of flight (t) = 2 * Vy / g
where g is the acceleration due to gravity (9.8 m/s^2)
Calculating the time of flight:
t = 2 * Vy / g
t = 2 * (84 * sin(45)) / 9.8
t ≈ 2 * 59.39 / 9.8
t ≈ 12.1 s
Now, we can determine the horizontal distance covered without air resistance using the formula:
Horizontal distance (D) = Vx * t
Calculating the horizontal distance without air resistance:
D = 59.39 * 12.1
D ≈ 718.84 m
So, the horizontal distance covered without air resistance is approximately 718.84 m.
Now let's calculate the percentage decrease caused by air resistance:
Percentage decrease = ((Horizontal distance without air resistance - Horizontal distance with air resistance) / Horizontal distance without air resistance) * 100
Given:
Observed horizontal distance with air resistance = 630 m
Calculating the percentage decrease:
Percentage decrease = ((718.84 - 630) / 718.84) * 100
Percentage decrease ≈ (88.84 / 718.84) * 100
Percentage decrease ≈ 12.34%
Therefore, the percentage decrease in the horizontal distance observed due to air resistance is approximately 12.34%.
Vo = 84m/s[45o].
Dx = Vo^2*sin(2A)/g=84^2*sin90/9.8=720 m
with zero wind.
(720-630)/720 * 100% = 12.5% Decrease.