Final answer:
To find the range, maximum height, and speed at impact of a projectile fired with an initial speed of 500m/s and angle of elevation 30 degrees, we can use the equations of projectile motion.
Step-by-step explanation:
To find the range, maximum height, and speed at impact of a projectile fired with an initial speed of 500m/s and angle of elevation 30 degrees, we can use the equations of projectile motion.
Range: The horizontal distance covered by the projectile is the range. In this case, we can use the formula:
R = (V02 * sin(2θ)) / g
where R is the range, V0 is the initial speed, θ is the angle of elevation, and g is the acceleration due to gravity.
Substituting the given values into the formula, we have:
R = (5002 * sin(2 * 30)) / 9.8
R = (250000 * sin(60)) / 9.8
R ≈ 1450.83 meters
Maximum Height: The maximum height reached by the projectile can be found using the formula:
H = (V02 * sin2(θ)) / (2 * g)
Substituting the given values into the formula:
H = (5002 * sin2(30)) / (2 * 9.8)
H ≈ 3060.45 meters
Speed at Impact: The speed at impact is the magnitude of the velocity of the projectile when it hits the ground. Since the projectile is fired at an angle and lands at a lower height than its initial position, the speed at impact will be lower than the initial speed. However, we need more information to calculate the exact speed at impact.