Question

A projectile is fired into the air at an angle of 33 degrees above ground level and hits a target downrange. At what other angle could it be fired to hit the target?

a) 57 degrees
b) 67 degrees
c) 47 degrees
d) 45 degrees

Answer 1

A projectile fired at 33 degrees can also be fired at the reciprocal angle of 57 degrees to hit the same target. The complementary angles with respect to 90 degrees will result in the same range on level ground.

Step-by-step explanation:

To determine the other angle at which a projectile could be fired to hit the same target, we need to understand projectile motion. According to the principles of physics, for any given initial speed, there are two angles of projection that allow a projectile to reach the same point on level ground. These angles are complementary with respect to 90 degrees. Hence, if a projectile is fired at an angle of θ, it can also be fired at an angle of (90 - θ) to reach the same point.

In this case, the projectile is fired at 33 degrees. Therefore, the complimentary angle to hit the same target would be 57 degrees (90 - 33 = 57). Hence the correct answer is a) 57 degrees.

GRASP CHECK

If a projectile is launched on level ground, the optimum angle to maximize the range is 45 degrees.