Thank you for visiting Albert is in an archery contest He is shooting for a target that is at the same height as the height he is shooting from. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
The problem is about projectile motion, a principle of physics. To find the two angles at which Albert can shoot to hit his target, we can use the formula for the range of a projectile launched at an angle, sin^-1((g*d) / (v^2)), where g is gravity, d is distance, and v is speed. The two resulting angles are complementary to each other.
Explanation:
Given that the distance, the speed, and the gravitational force, but not the angle, are known, this problem involves the principles of projectile motion. In physics, when a body is thrown into space with an angle to the horizontal, it follows a parabolic path called trajectory. The body performs two movements: horizontal uniform motion and vertically accelerated motion. The two angles at which Albert can shoot to hit the target are calculated with the following formula: sin^-1((g*d) / (v^2)) where g is gravity (9.81 m/s^2), d is distance (85 m) and v is the initial speed (67 m/s).
The two solutions to this equation, due to the property of sine function which has two angles in the range of 0 to 180 that have the same sine values, are therefore the two angles that Albert can use to hit the target. These angles are complementary, meaning they add up to 90 degrees, since they are two angles across from each other in the right triangle.
Learn more about Projectile Motion here:
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