An anticraft shell is fired vertically upward with a muzzle velocity of 1000m/s.calculate when its height will be 37.5km
To calculate when the height of the anti-craft shell will be 37.5 km, we can use the equations of motion. We know that the initial velocity (u) is 1000 m/s and the final velocity (v) is 0 m/s since the shell reaches its highest point and then falls back down. The acceleration (a) due to gravity is approximately -9.8 m/s^2 (negative because it acts in the opposite direction to the initial velocity).
To find the time taken (t), we can use the second equation of motion:
v = u + at
Substituting the known values:
0 = 1000 - 9.8t
9.8t = 1000
t = 1000/9.8
t ≈ 102.04 seconds
So, it would take around 102.04 seconds for the anti-craft shell to reach its maximum height.
Now, to calculate the maximum height (h) reached by the shell, we can use the third equation of motion:
v^2 = u^2 + 2ah
Substituting the known values:
0 = (1000)^2 + 2(-9.8)h
h = (1000)^2 / (2 * 9.8)
h ≈ 5091.8 meters (or 5.0918 km)
Therefore, the maximum height reached by the anti-craft shell is approximately 5.0918 km.
To find when the height will be 37.5 km, we need to calculate the time it takes to reach that height from the initial position. Since the shell reaches its maximum height in approximately 102.04 seconds and then falls back down symmetrically, it will take a similar amount of time to return to the initial height. So the total time is approximately 2 * 102.04 = 204.08 seconds.
Therefore, it will take around 204.08 seconds for the anti-craft shell to reach a height of 37.5 km.