A projectile is launched at an angle of 30 degrees with an initial speed of 20 m

A projectile is launched at an angle of 30 degrees with an initial speed of 20 m/s. What is the maximum height reached by the projectile?

A projectile is launched at an angle of 30 degrees with an initial speed of 20 m/s. What is the maximum height reached by the projectile?

Step 1: Identify the given values. The initial speed (u) is 20 m/s, the angle (θ) is 30 degrees, and the acceleration due to gravity (g) is 9.8 m/s².
Step 2: Convert the angle from degrees to radians if necessary, but here we can use the sine function directly for 30 degrees.
Step 3: Calculate sin(30 degrees). The sine of 30 degrees is 0.5.
Step 4: Use the formula for maximum height: h = (u² * sin²θ) / (2g).
Step 5: Substitute the values into the formula. First, calculate u²: 20² = 400.
Step 6: Calculate sin²(30 degrees): (0.5)² = 0.25.
Step 7: Now substitute into the formula: h = (400 * 0.25) / (2 * 9.8).
Step 8: Calculate the numerator: 400 * 0.25 = 100.
Step 9: Calculate the denominator: 2 * 9.8 = 19.6.
Step 10: Now divide the numerator by the denominator: h = 100 / 19.6.
Step 11: Calculate the final result: h ≈ 5.1 m.

Projectile Motion – The study of the motion of an object that is launched into the air and influenced only by gravity and its initial velocity.
Kinematic Equations – Equations that describe the motion of objects, particularly useful in calculating maximum height, range, and time of flight for projectiles.
Trigonometry in Physics – The use of sine and cosine functions to resolve the initial velocity into horizontal and vertical components.