A 5.2 kg projectile is launched from a launching device. It leaves the launcher traveling at 4000 m/s. The net force during the launch was equal to 4.3×105 Newtons. How much time did the project spend in the launcher?
To determine the time the projectile spent in the launcher, we need to use the equation describing the relationship between force, mass, and acceleration. This equation is:
F = m * a
Where F is the force, m is the mass, and a is the acceleration.
In this case, we know the force (F) is equal to 4.3 × 10^5 Newtons, and the mass (m) is 5.2 kg.
We can rearrange the equation to solve for acceleration:
a = F / m
Plugging in the values:
a = (4.3 × 10^5 N) / (5.2 kg)
Now, since we know the projectile started from rest and accelerated to a final velocity of 4000 m/s, we can use the equation that relates acceleration, time, and final velocity:
v = a * t
Where v is the final velocity, a is the acceleration, and t is the time.
Since the projectile started from rest, the initial velocity (u) is 0 m/s.
Plugging in the values:
4000 m/s = (4.3 × 10^5 N / 5.2 kg) * t
Now, we can solve for t:
t = 4000 m/s / (4.3 × 10^5 N / 5.2 kg)
Calculating this value:
t ≈ 0.011628 s
Therefore, the projectile spent approximately 0.011628 seconds in the launcher.