Hayes fires a projectile from his air gun. The gun provides a constant 300 N of force on a 0.1 kg projectile as it travels through the 0.3 meter barrel. How fast is it going when it leaves? It starts from rest and there is no friction.
To find the speed of the projectile when it leaves the barrel, we can use the equation:
Force (F) = mass (m) * acceleration (a)
Given:
Force = 300 N
Mass = 0.1 kg
Since the force provided by the air gun is constant throughout, we can assume that the acceleration is also constant.
Thus, we have:
300 N = 0.1 kg * a
Now, we need to find the acceleration.
We can rearrange the formula to solve for acceleration:
a = Force / Mass
Substituting the given values, we have:
a = 300 N / 0.1 kg = 3000 m/s^2
Now that we have the acceleration, we can use another equation to find the final velocity (v) of the projectile:
v^2 = u^2 + 2as
Where:
v is the final velocity
u is the initial velocity (which is 0 m/s since it starts from rest)
a is the acceleration (3000 m/s^2)
s is the distance traveled in the barrel (0.3 meters)
Plugging in the values, we get:
v^2 = 0^2 + 2 * 3000 m/s^2 * 0.3 m
v^2 = 0 + 1800 m^2/s^2
v^2 = 1800 m^2/s^2
To find v, we can take the square root of both sides:
v = √1800 m/s
v ≈ 42.43 m/s
Therefore, the projectile is going approximately 42.43 m/s when it leaves the barrel.