To solve this problem, we can use the equations of motion for projectile motion.

(a) The time of flight of the projectile can be calculated using the equation:

Time of flight = 2 * (Initial velocity * sin(angle)) / acceleration due to gravity

Here, the initial velocity (u) is given as 85 meters/second, the angle (θ) is given as 40 degrees, and the acceleration due to gravity (g) is approximately 9.8 meters/second^2.

Using these values, we can calculate the time of flight:

Time of flight = 2 * (85 * sin(40)) / 9.8
Time of flight ≈ 11.15 seconds

Therefore, the time of flight of the projectile is approximately 11.15 seconds.

(b) The height of the trajectory can be calculated using the equation:

Height = (Initial velocity^2 * (sin(angle))^2) / (2 * acceleration due to gravity)

Using the given values:

Height = (85^2 * (sin(40))^2) / (2 * 9.8)
Height ≈ 144.01 meters

Therefore, the height of the trajectory is approximately 144.01 meters.

(c) The range can be calculated using the equation:

Range = (Initial velocity^2 * sin(2 * angle)) / acceleration due to gravity

Using the given values:

Range = (85^2 * sin(2 * 40)) / 9.8
Range ≈ 619.5 meters

Therefore, the range of the projectile is approximately 619.5 meters.

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