Question

A bullet is fired from a gun with muzzle velocity at 200m/s at angle 60 degrees to horizontal. What is the range, maximum height reached, and time in flight?

Answer 1

To find the range, maximum height, and time of flight of a bullet fired from a gun, we can use the equations of projectile motion. Let's calculate each of these values step by step:

1. Range: The range is the horizontal distance traveled by the bullet. We can calculate it using the formula:

Range = (Initial velocity² * sin(2θ)) / g

where:

• Initial velocity is the muzzle velocity of the bullet (200 m/s).
• θ is the launch angle (60 degrees).
• g is the acceleration due to gravity (approximately 9.8 m/s²).

Substituting the values into the formula:

Range = (200² * sin(2 * 60)) / 9.8 Range = (40,000 * sin(120)) / 9.8 Range = (40,000 * sin(60)) / 9.8 Range = (40,000 * √3/2) / 9.8 Range = 2 * (40,000 * √3) / 9.8 Range ≈ 2 * 2438.78 Range ≈ 4877.56 meters

So, the range of the bullet is approximately 4877.56 meters.

2. Maximum height: The maximum height reached by the bullet can be calculated using the formula:

Maximum height = (Initial velocity² * sin²(θ)) / (2 * g)

Substituting the values into the formula:

Maximum height = (200² * sin²(60)) / (2 * 9.8) Maximum height = (40,000 * (√3/2)²) / (2 * 9.8) Maximum height = (40,000 * 3/4) / (2 * 9.8) Maximum height = (30,000) / (19.6) Maximum height ≈ 1530.61 meters

So, the maximum height reached by the bullet is approximately 1530.61 meters.

3. Time of flight: The time of flight is the total duration the bullet remains in the air. We can calculate it using the formula:

Time of flight = (2 * Initial velocity * sin(θ)) / g

Substituting the values into the formula:

Time of flight = (2 * 200 * sin(60)) / 9.8 Time of flight = (400 * √3/2) / 9.8 Time of flight = (400 * √3) / (2 * 9.8) Time of flight ≈ (400 * √3) / 19.6 Time of flight ≈ 6.72 seconds

So, the time of flight of the bullet is approximately 6.72 seconds.