An object is thrown at an angle of 30 degrees with a speed of 40 m/s. What is th

An object is thrown at an angle of 30 degrees with a speed of 40 m/s. What is the time of flight until it returns to the same vertical level?

An object is thrown at an angle of 30 degrees with a speed of 40 m/s. What is the time of flight until it returns to the same vertical level?

Step 1: Identify the given values. The speed (u) is 40 m/s and the angle (θ) is 30 degrees.
Step 2: Convert the angle from degrees to radians if necessary, but here we can use the sine directly.
Step 3: Calculate the sine of the angle. sin(30 degrees) = 0.5.
Step 4: Use the formula for time of flight: T = (2 * u * sin(θ)) / g.
Step 5: Substitute the values into the formula: T = (2 * 40 * 0.5) / 9.8.
Step 6: Calculate the numerator: 2 * 40 * 0.5 = 40.
Step 7: Divide the result by g (acceleration due to gravity, approximately 9.8 m/s²): T = 40 / 9.8.
Step 8: Perform the division: T ≈ 4.08 seconds.

Projectile Motion – The question tests understanding of the time of flight for a projectile launched at an angle, using the formula that incorporates initial velocity, angle of projection, and acceleration due to gravity.
Trigonometric Functions – The use of sine function to resolve the vertical component of the initial velocity is crucial for calculating the time of flight.
Kinematics – The application of kinematic equations to determine the time of flight based on vertical motion.