An aircraft is fired vertically upwards with a muzzle velocity of 100m/s calculate :
A)the maximum height it can attain
B)the time taken to reach this height
It must be exciting to be aboard that aircraft, almost like a projectile
Easy way - use conservation of energy
(1/2)m v^2 = m g h
h = v^2/2g
and for time:
v = 100 - 9.81 t
at top v = 0
t = 100/9.81 or about ten seconds
I want the solving
An anticraft shell is fired vertical upward with a muzzle velocity m/s .
To calculate the maximum height the aircraft can attain and the time taken to reach this height, you can use the equations of motion for vertical motion.
Let's break it down step by step:
A) To calculate the maximum height the aircraft can attain:
1. Identify the initial velocity (u) as 100 m/s (given).
2. Determine the acceleration (a). In this case, gravity is acting as the acceleration, so the value of acceleration (a) is approximately 9.8 m/s² (assuming the motion is near the surface of Earth).
3. Use the formula for calculating the maximum height (h) reached by an object in free-fall motion:
h = (u² - v²) / (2a)
Since the aircraft is fired vertically upwards, the final velocity (v) at the maximum height is zero. So, the formula becomes:
h = (u²) / (2a)
Substituting the values:
h = (100²) / (2 * 9.8)
= 5000 / 19.6
≈ 255.1 meters
Therefore, the maximum height the aircraft can attain is approximately 255.1 meters.
B) To calculate the time taken to reach this height:
1. Identify the initial velocity (u) as 100 m/s (given).
2. Determine the acceleration (a) as approximately 9.8 m/s².
3. Use the formula for calculating the time (t) taken to reach a certain height:
h = ut + (1/2)at²
Since we are interested in the time taken to reach the maximum height, we can substitute the height (h) with the value obtained in part A (approximately 255.1 m):
255.1 = 100t + (1/2)(9.8)t²
Simplify the equation:
0.5(9.8)t² + 100t - 255.1 = 0
This is a quadratic equation in terms of time (t). You can solve it using the quadratic formula or by factoring. Once you find the value of t, it will give you the time taken to reach the maximum height.
Solving this equation, we find:
t ≈ 5.15 seconds
Therefore, the time taken for the aircraft to reach the maximum height is approximately 5.15 seconds.