What two angles of elevation will enable a projectile to reach a target 16 km downrange on the same level as the gun if the projectile's initial speed is 400m/sec ?
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To determine the two angles of elevation that will allow a projectile to reach a target 16 km away with an initial speed of 400 m/s, we can use the equations of projectile motion.
First, let's convert the range from kilometers to meters:
16 km = 16,000 meters
We also know the initial velocity of the projectile is 400 m/s.
The range of a projectile can be calculated using the formula:
range = (initial velocity^2 * sine(2 * angle of elevation)) / gravitational acceleration
In this case, the range is 16,000 meters.
Now, we can rearrange the formula to solve for the angle of elevation:
angle of elevation = (arcsine((range * gravitational acceleration) / initial velocity^2)) / 2
Using this formula, we can calculate the angles of elevation required to reach the target.
1. Calculate the first angle of elevation:
angle of elevation 1 = (arcsine((16,000 * 9.8) / (400^2))) / 2
2. Calculate the second angle of elevation:
angle of elevation 2 = π - angle of elevation 1
Note: The reason for subtracting the angle of elevation 1 from π is that the projectile can be launched at two symmetrical angles to reach the same range, with one angle above the horizontal (angle of elevation 1) and the other below the horizontal (angle of elevation 2).
After evaluating the above formulas using a calculator, you will find the two angles of elevation that enable the projectile to reach the target 16 km downrange with an initial speed of 400 m/s.