A rifle is shot with 30.0m for distance and hit's a target at 1.90cm as a height. What is the flight time? What is the velocity of the shot?

To calculate the flight time and velocity of the shot, we can use basic principles of projectile motion.

Let's assume that the rifle is shot horizontally, without any vertical initial velocity. In that case, the horizontal distance travelled by the shot is equal to the muzzle velocity multiplied by the flight time.

First, let's convert the given distance and height into meters:

Distance = 30.0 m
Height = 1.90 cm = 0.019 m

To calculate the flight time, we need to find out the time it takes for the shot to travel a horizontal distance of 30.0 m.

We can use the formula for horizontal distance:
Distance = Velocity * Time

In this case, the vertical height does not affect the horizontal displacement, so we can ignore it for now.

So, rearranging the formula:
Time = Distance / Velocity

Now, let's calculate the flight time:
Time = 30.0 m / Velocity

Next, to calculate the velocity of the shot, we need to consider the vertical motion. Since we are given the height, we can use the formula for vertical displacement:

Vertical displacement = (1/2) * acceleration * Time^2

Assuming there's no air resistance, the vertical acceleration is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2.

In this case, the vertical displacement is given as 0.019 m.

By plugging in the values, we get:
0.019 m = (1/2) * 9.8 m/s^2 * Time^2

Simplifying the equation:
0.019 m = 4.9 m/s^2 * Time^2

Now, we have two equations:
Time = 30.0 m / Velocity
0.019 m = 4.9 m/s^2 * Time^2

By substituting the value of Time from the first equation into the second equation, we can solve for Velocity.

0.019 m = 4.9 m/s^2 * (30.0 m / Velocity)^2

Simplifying and rearranging the equation, we have:

Velocity^2 = (4.9 m/s^2 * (30.0 m)^2) / 0.019 m

Now, we can find the value of Velocity:
Velocity = sqrt((4.9 m/s^2 * (30.0 m)^2) / 0.019 m)

Plugging these values into a calculator, we find the answer.