A ball is thrown at an angle of 30 degrees with a speed of 30 m/s. What is the t

A ball is thrown at an angle of 30 degrees with a speed of 30 m/s. What is the time of flight until it hits the ground?

A ball is thrown at an angle of 30 degrees with a speed of 30 m/s. What is the time of flight until it hits the ground?

Step 1: Identify the initial speed (u) of the ball, which is given as 30 m/s.
Step 2: Identify the angle of projection (θ), which is given as 30 degrees.
Step 3: Convert the angle from degrees to radians if necessary, but here we can use the sine directly.
Step 4: Calculate the sine of the angle: sin(30 degrees) = 0.5.
Step 5: Identify the acceleration due to gravity (g), which is approximately 9.8 m/s².
Step 6: Use the formula for time of flight (T): T = (2 * u * sin(θ)) / g.
Step 7: Substitute the values into the formula: T = (2 * 30 * 0.5) / 9.8.
Step 8: Calculate the numerator: 2 * 30 * 0.5 = 30.
Step 9: Divide the numerator by g: 30 / 9.8 ≈ 3.06.
Step 10: Conclude that the time of flight until the ball hits the ground is approximately 3.06 seconds.

Projectile Motion – The question tests understanding of the time of flight for a projectile launched at an angle, using the formula T = (2u * sin(θ))/g.
Trigonometry in Physics – It requires knowledge of how to calculate the vertical component of the initial velocity using the sine function.
Gravity's Role – The effect of gravitational acceleration (g) on the time of flight is a key concept.