A ball is thrown at an angle of 45 degrees with an initial speed of 14 m/s. What

A ball is thrown at an angle of 45 degrees with an initial speed of 14 m/s. What is the range of the projectile?

A ball is thrown at an angle of 45 degrees with an initial speed of 14 m/s. What is the range of the projectile?

Step 1: Identify the initial speed (u) of the ball, which is 14 m/s.
Step 2: Identify the angle of projection (θ), which is 45 degrees.
Step 3: Convert the angle to radians if necessary, but for 45 degrees, sin(2θ) = sin(90 degrees) = 1.
Step 4: Identify the acceleration due to gravity (g), which is approximately 9.8 m/s².
Step 5: Use the range formula for projectile motion: R = (u² * sin(2θ)) / g.
Step 6: Substitute the values into the formula: R = (14² * 1) / 9.8.
Step 7: Calculate 14², which is 196.
Step 8: Divide 196 by 9.8 to find the range: R ≈ 20 m.

Projectile Motion – The motion of an object thrown into the air, subject to gravitational acceleration, analyzed using kinematic equations.
Range of a Projectile – The horizontal distance traveled by a projectile, calculated using the initial speed, launch angle, and acceleration due to gravity.
Trigonometric Functions in Physics – Understanding how to apply sine and cosine functions to resolve components of motion in projectile problems.