Final answer:
The range of the projectile is approximately 8850 meters, the max height reached is about 647 meters, and the time of flight is approximately 237.4 seconds.
Step-by-step explanation:
To find the range, we need to calculate the horizontal distance traveled by the projectile. The range can be found using the formula:
Range = (Initial Velocity * Initial Velocity * sin(2 * Angle of Launch)) / g
where g is the acceleration due to gravity (9.8 m/s^2). Substituting the values, we get:
Range = (1000 * 1000 * sin(2 * 42)) / 9.8 ≈ 8850 meters.
To find the max height, we need to calculate the vertical displacement of the projectile. The max height can be found using the formula:
Max Height = (Initial Velocity * Initial Velocity * sin(Angle of Launch)^2) / (2 * g)
Substituting the values, we get:
Max Height = (1000 * 1000 * sin(42)^2) / (2 * 9.8) ≈ 647 meters.
To find the time of flight, we can calculate the time it takes for the projectile to reach its highest point and then double it. The time to reach the highest point can be found using the formula:
Time to Reach Highest Point = Initial Velocity * sin(Angle of Launch) / g
Substituting the values, we get:
Time to Reach Highest Point = 1000 * sin(42) / 9.8 ≈ 118.7 seconds.
Since the total time of flight is double the time to reach the highest point, the time of flight is approximately 2 * 118.7 ≈ 237.4 seconds.