A man shots a rifle with 30.m and hit's an object at 1.90cm. What is the flight time? What is the velocity of the shot?
1.90=.19m
To calculate the flight time and velocity of the shot, we can use the basic equations of projectile motion. The key equation for projectile motion is:
y = ut + (1/2)at^2
Where:
- y is the vertical displacement (in meters) of the object from its initial position
- u is the initial velocity (in meters per second) of the object
- t is the time (in seconds)
- a is the acceleration (in meters per second squared) due to gravity, which is approximately 9.8 m/s^2.
In this case, we assume that the object is launched horizontally, which means it has no initial vertical velocity (u = 0).
To find the flight time:
1) We can set y as the vertical displacement of the object, which is given as 1.90 meters.
1.90 = (1/2) * 9.8 * t^2
2) Rearrange the equation to solve for the flight time (t):
t^2 = (1.90 * 2) / 9.8
t^2 = 0.3878
t ≈ √0.3878
t ≈ 0.6237 seconds
So, the flight time is approximately 0.6237 seconds.
To find the velocity of the shot:
1) We can use the formula for horizontal distance traveled (x) by an object in projectile motion:
x = ut
2) Rearrange the equation to solve for the initial velocity (u):
u = x / t
Given that the horizontal distance (x) is 30 meters and the flight time (t) is 0.6237 seconds, we can substitute these values into the equation to find the initial velocity (u):
u = 30 / 0.6237
u ≈ 48.07 m/s
So, the velocity of the shot is approximately 48.07 m/s.