A projectile is launched with an initial velocity of 30 m/s at an angle of 30 de
Practice Questions
Q1
A projectile is launched with an initial velocity of 30 m/s at an angle of 30 degrees. What is the horizontal range of the projectile? (Take g = 10 m/s²)
90 m
75 m
100 m
120 m
Questions & Step-by-Step Solutions
A projectile is launched with an initial velocity of 30 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 30 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 = (30² * sin(60 degrees)) / 10.
Step 6: Calculate 30², which is 900.
Step 7: Find sin(60 degrees), which is √3/2.
Step 8: Substitute sin(60 degrees) into the equation: R = (900 * √3/2) / 10.
Step 9: Simplify the equation: R = (900 * √3) / 20.
Step 10: Calculate 900 / 20, which is 45, so R = 45√3 m.
Step 11: If needed, approximate 45√3 m to a numerical value, which is approximately 90 m.
Projectile Motion – The motion of an object thrown into the air, subject to gravitational acceleration, characterized by its initial velocity, launch angle, and the effects of gravity.
Range of a Projectile – The horizontal distance traveled by a projectile, calculated using the formula R = (u² * sin(2θ))/g, where u is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.
Trigonometric Functions – Understanding and applying sine and cosine functions to resolve the components of the initial velocity into horizontal and vertical components.
