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Complete Question
A gas gun uses high pressure gas tp accelerate projectile through the gun barrel.
If the acceleration of the projective is : a = c/s m/s2
Where c is a constant that depends on the initial gas pressure behind the projectile. The initial position of the projectile is s= 1.5m and the projectile is initially at rest. The projectile accelerates until it reaches the end of the barrel at s=3m. What is the value of the constant c such that the projectile leaves the barrel with velocity of 200m/s?
Answer:
The value of the constant is
Explanation:
From the question we are told that
The acceleration is
The initial position of the projectile is s= 1.5m
The final position of the projectile is
The velocity is
Generally
and acceleration is
so
=>
integrating both sides
Now for the limit
a = 200 m/s
b = 0 m/s
c = s= 3 m
d == 1.5 m
So we have
=>