A gun shoots a bullet at 1200 m/s at an angle of 600 above the horizontal. Neglecting air resistance, determine:
a.) its time of flight
b.) its range
To determine the time of flight and range of the bullet, we can break the initial velocity into its horizontal and vertical components.
The horizontal component (Vx) can be found using the equation:
Vx = V * cos(θ)
where V is the initial velocity of the bullet (1200 m/s) and θ is the angle above the horizontal (60°).
Vx = 1200 m/s * cos(60°)
Vx = 1200 m/s * 0.5
Vx = 600 m/s
The vertical component (Vy) can be found using the equation:
Vy = V * sin(θ)
Vy = 1200 m/s * sin(60°)
Vy = 1200 m/s * √(3/2)
Vy = 1200 m/s * 0.866
Vy ≈ 1039.23 m/s
a.) Time of Flight:
The time of flight can be determined using the vertical component of velocity. We can use the equation:
Vy = a * t
where a is the acceleration due to gravity (-9.8 m/s²) and t is the time of flight.
1039.23 m/s = -9.8 m/s² * t
Solving for t, we get:
t = -1039.23 m/s / -9.8 m/s²
t ≈ 106 seconds (rounded to two decimal places)
b.) Range:
The range of the bullet can be determined using the horizontal component of velocity and the time of flight. We can use the equation:
Range = Vx * t
Range = 600 m/s * 106 s
Range ≈ 63,600 meters or 63.6 kilometers (rounded to two decimal places)
Therefore, the time of flight is approximately 106 seconds and the range of the bullet is approximately 63.6 kilometers.