A ball is thrown at an angle of 30 degrees with an initial speed of 25 m/s. What

A ball is thrown at an angle of 30 degrees with an initial speed of 25 m/s. What is the time to reach the maximum height?

A ball is thrown at an angle of 30 degrees with an initial speed of 25 m/s. What is the time to reach the maximum height?

Step 1: Identify the initial speed (u) of the ball, which is 25 m/s.
Step 2: Identify the angle (θ) at which the ball is thrown, which is 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 vertical component of the initial speed using the formula: u * sin(θ). For 30 degrees, sin(30) = 1/2.
Step 5: Calculate the vertical component: 25 m/s * (1/2) = 12.5 m/s.
Step 6: Identify the acceleration due to gravity (g), which is approximately 9.8 m/s².
Step 7: Use the formula to find the time to reach maximum height: t = (u * sin(θ)) / g.
Step 8: Substitute the values into the formula: t = (12.5 m/s) / (9.8 m/s²).
Step 9: Calculate the time: t ≈ 1.28 seconds.

Projectile Motion – The question tests understanding of the time to reach maximum height in projectile motion, which involves the initial velocity, launch angle, and acceleration due to gravity.
Trigonometric Functions – The use of sine function to resolve the initial velocity into vertical and horizontal components is essential for solving the problem.
Kinematics – Application of kinematic equations to determine the time taken to reach the maximum height based on vertical motion.