A dart gun is located 1 meter above the floor and is fired horizontally. the dart travels a horizontal distance of 4 meters when it hits the floor. what is the initial velocity if the dart when fired?
L=v(x)•t => t=L/v(x)
h=gt²/2 = gL²/2v(x)²
v(x)= sqrt (gL²/2h)
To find the initial velocity of the dart, we can use the concept of projectile motion and the equations of motion. In this case, since the dart is fired horizontally, the initial vertical velocity is 0 m/s.
We can use the equation:
d = v * t,
where:
d is the horizontal distance (4 meters),
v is the initial horizontal velocity (what we want to find), and
t is the time it takes for the dart to hit the floor.
Since the vertical distance traveled by the dart is equal to the height from which it was fired (1 meter), we can use the equation:
d = (1/2) * g * t^2,
where:
g is the acceleration due to gravity (approximately 9.8 m/s^2).
By rearranging this equation, we can express t in terms of d:
t = √(2d / g).
Now, we can substitute this value of t into the equation for the horizontal distance:
d = v * (√(2d / g)),
Simplifying this equation, we get:
v = d / √(2d / g).
Now, let's calculate the value of v:
v = 4 / √(2 * 4 / 9.8),
v = 4 / √(8 / 9.8),
v = 4 / √(0.816),
v ≈ 4 / 0.903,
v ≈ 4.43 m/s.
Therefore, the initial velocity of the dart when fired is approximately 4.43 m/s.