Projectile Motion and Range Analysis

The video tutorial explains the derivation and application of the range formula in physics, which calculates the horizontal displacement of a projectile. The instructor demonstrates how to use the formula with example problems, including calculating the angle needed to hit a target at a specific distance. The concept of complementary angles is explored, showing how different angles can result in the same range. The tutorial emphasizes understanding the physics behind the calculations rather than just hitting a target.

What is the primary purpose of the range formula in projectile motion?

• To calculate the time of flight

• To determine the maximum height

• To find the horizontal displacement

• To measure the initial velocity

In the example problem, what is the initial velocity of the projectile?

• 15 meters per second

• 18 meters per second

• 12 meters per second

• 10 meters per second

What angle was used in the example problem to achieve a range of approximately 14.7 meters?

• 30 degrees

• 45 degrees

• 60 degrees

• 90 degrees

To hit a target 15 meters away with a speed of 18 m/s, what angle should the projectile be fired at?

• 10 degrees

• 13.5 degrees

• 25 degrees

• 20 degrees

What is the sine of twice the angle when the angle is 13.5 degrees?

• 0.454

• 0.544

• 0.867

• 1.000

Which pair of angles are complementary and provide the same range?

• 15 and 75 degrees

• 20 and 70 degrees

• 30 and 60 degrees

• 45 and 45 degrees

What is the sine of twice the angle for a 30-degree launch angle?

• 1.000

• 0.867

• 0.707

• 0.500

What is the optimal angle for achieving the maximum range in projectile motion without air resistance?

• 60 degrees

• 30 degrees

• 90 degrees

• 45 degrees

What happens to the range of a projectile when fired at complementary angles?

• The range is doubled

• The range is zero

• The range is halved

• The range remains the same

What factor is not considered in the range formula that affects real-world projectile motion?

• Initial velocity

• Launch angle

• Air resistance

• Gravity