Calculate the maximum height the tank shell reaches using the initial speed (18 m/s), half-time(1.8), and angle(75).
To calculate the maximum height the tank shell reaches, we can use the equations of projectile motion. First, we need to break down the initial velocity into its horizontal and vertical components.
Given:
Initial speed (vi) = 18 m/s
Half-time (t/2) = 1.8 seconds
Angle (θ) = 75 degrees
Horizontal component of velocity (vix):
vix = vi * cos(θ)
Vertical component of velocity (viy):
viy = vi * sin(θ)
Next, we need to find the time it takes for the shell to reach its maximum height. Since we are given the half-time (t/2), we can calculate the total time (t):
t = 2 * (t/2)
Now, we can use the equation of motion to find the maximum height (hmax):
hmax = viy^2 / (2 * g)
Where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Let's calculate the values step by step:
1. Calculate the horizontal component of velocity (vix):
vix = 18 * cos(75)
2. Calculate the vertical component of velocity (viy):
viy = 18 * sin(75)
3. Calculate the total time (t):
t = 2 * 1.8
4. Calculate the maximum height (hmax):
hmax = (viy^2) / (2 * g)
Now, let's substitute the values into the equations:
vix = 18 * cos(75) ≈ 18 * 0.258819 = 4.658 m/s
viy = 18 * sin(75) ≈ 18 * 0.965926 = 17.388 m/s
t = 2 * 1.8 = 3.6 seconds
hmax = (17.388^2) / (2 * 9.8) ≈ 301.183 / 19.6 = 15.37 meters
Therefore, the maximum height the tank shell reaches is approximately 15.37 meters.