In 1346 the army of King Edward III of England defeated the forces of King Phillip VI of France at the battle of Crecy.The following passage gives some details:
The main reason for Edward III's success was undoubtedly the longbow. The records say that skilled long bowmen could fire as many as 12 arrows a minute- with up to 3 arrows in the air at the same time. They were said to have a lethal effect at a range of 300m.
A) The time of flight was about 10s. Assuming the path of the arrow was symmetrical show that the initial vertical component of the arrow's velocity was about 50ms-1.
B) If these arrows were fired at 50 degrees to the horizontal, calculate the velocity at which they left the longbow.
c)Show that the theoretical range was about 400m.
d)The range calculated is greater than 300m quoted in the passage. State and explain some possile reasons for the difference in the answers.
PLEASE help in a simple and detaileld way because i am really confused
a. Tr+Tf = 10 s. = Time in air.
Tr = Tf, Tr+Tr = 10, Tr = 5 s. = Rise time.
Y = Yo + g*Tr = 0 @ max ht.
Yo + (-9.8)*5 = 0
Yo = 49 m/s or about 50 m/s.
b. Yo = Vo*sin50 = 49.
Vo = 49/sin50 = 64.0 m/s.
c. Xo = Vo*Cos50 = 64*Cos50 = 41.1 m/s.
Range = Xo*(Tr+Tf) = 41.1 * 10 = 411 m.
d. The range was said to have a lethal
effect at 300 meters, but it didn't say that was the max range.
I dont get all these tf, tr, yo terms you used please expain more clearly i dont understant it
Vo = Initial velocity.
Xo = Horizontal component of initial velocity.
Yo = Vertical component of initial velocity.
Tr = Rise time or time to reach max. height.
Tf = Fall time.
A) To find the initial vertical component of the arrow's velocity, we need to use the equation for time of flight. The equation is:
time of flight = 2 * (initial vertical component of velocity) / acceleration due to gravity
Given that the time of flight is about 10 seconds and the acceleration due to gravity is about 9.8 m/s^2, we can rearrange the equation to solve for the initial vertical component of velocity:
(initial vertical component of velocity) = (time of flight * acceleration due to gravity) / 2
Substituting the given values, we have:
(initial vertical component of velocity) = (10 s * 9.8 m/s^2) / 2
Simplifying the equation, we get:
(initial vertical component of velocity) = 49 m/s
Therefore, the initial vertical component of the arrow's velocity is about 49 m/s or approximately 50 m/s.
B) To calculate the velocity at which the arrows left the longbow, we can use the components of velocity and trigonometry. The initial velocity can be separated into its horizontal component (Vx) and vertical component (Vy). Given that the arrows were fired at 50 degrees to the horizontal, we can calculate the velocity using the following equations:
Vx = velocity * cos(angle)
Vy = velocity * sin(angle)
Since the angle is given as 50 degrees and we want to find the velocity, we use the equation:
velocity = Vx / cos(angle)
Substituting the values, we have:
velocity = Vx / cos(50 degrees)
Now, we need to calculate the horizontal component of velocity, Vx:
Vx = velocity * cos(angle)
Vx = velocity * cos(50 degrees)
Therefore, the velocity at which the arrows left the longbow can be calculated using trigonometry.
C) To show that the theoretical range was about 400m, we can use the equations of projectile motion. The range is the horizontal distance covered by the arrow. The equation for range is:
range = (initial horizontal component of velocity) * (time of flight)
Given that the time of flight is about 10 seconds and we need to find the initial horizontal component of velocity, we rearrange the equation:
(initial horizontal component of velocity) = range / (time of flight)
Substituting the values, we have:
(initial horizontal component of velocity) = 400m / 10s
Therefore, the initial horizontal component of velocity is approximately 40 m/s.
D) The range calculated is greater than the 300m quoted in the passage. There are several possible reasons for this difference:
1. Inaccuracy in historical records: The quoted range of 300m might not be entirely accurate due to historical record-keeping limitations. It's possible that the actual range was closer to what was calculated.
2. Variation in archers' skill: The range achieved with a longbow can vary depending on the archer's skill and proficiency. Skilled archers might have been able to achieve greater ranges, while less skilled ones might have had shorter ranges.
3. Environmental factors: The range of an arrow can be influenced by environmental factors such as wind speed and direction. These factors could have affected the actual range achieved in the battle.
4. Different arrow types: The range could vary depending on the type of arrows used. If different arrows were used during the battle of Crecy, it's possible that they had different ranges.
Overall, the calculation provides an estimation of the range based on the given information and assumptions.