A projectile is launched with an initial velocity of 40 m/s at an angle of 30 de
Practice Questions
Q1
A projectile is launched with an initial velocity of 40 m/s at an angle of 30 degrees. What is the horizontal range of the projectile? (Take g = 10 m/s²)
160 m
200 m
80 m
120 m
Questions & Step-by-Step Solutions
A projectile is launched with an initial velocity of 40 m/s at an angle of 30 degrees. What is the horizontal range of the projectile? (Take g = 10 m/s²)
Step 1: Identify the initial velocity (u) of the projectile, which is given as 40 m/s.
Step 2: Identify the launch angle (θ) of the projectile, which is given as 30 degrees.
Step 3: Calculate 2θ, which is 2 * 30 degrees = 60 degrees.
Step 4: Use the formula for the range of a projectile: R = (u² * sin(2θ)) / g.
Step 5: Substitute the values into the formula: R = (40² * sin(60 degrees)) / 10.
Step 6: Calculate 40², which is 1600.
Step 7: Find sin(60 degrees), which is √3/2.
Step 8: Substitute sin(60 degrees) into the equation: R = (1600 * √3/2) / 10.
Step 9: Simplify the equation: R = (1600 * √3) / 20.
Step 10: Calculate 1600 / 20, which is 80, so R = 80√3.
Step 11: To find the approximate value, calculate 80 * √3, which is approximately 138.56 m.
Projectile Motion – The study of the motion of an object that is launched into the air and is subject to gravitational acceleration.
Range of a Projectile – The horizontal distance traveled by a projectile when launched at a specific angle and initial velocity.
Trigonometric Functions – Understanding how to apply sine and cosine functions to resolve components of motion.
