A projectile is launched at an angle of 30° with an initial speed of 40 m/s. Wha

A projectile is launched at an angle of 30° with an initial speed of 40 m/s. What is the maximum height reached by the projectile?

A projectile is launched at an angle of 30° with an initial speed of 40 m/s. What is the maximum height reached by the projectile?

Step 1: Identify the given values. The initial speed (u) is 40 m/s, the angle (θ) is 30°, 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°.
Step 3: Calculate sin(30°). The sine of 30 degrees is 0.5.
Step 4: Calculate sin²(30°). This is (0.5)² = 0.25.
Step 5: Plug the values into the formula for maximum height: H = (u² * sin²θ) / (2g).
Step 6: Calculate u². This is (40 m/s)² = 1600 m²/s².
Step 7: Multiply u² by sin²(30°): 1600 m²/s² * 0.25 = 400 m²/s².
Step 8: Calculate 2g. This is 2 * 9.8 m/s² = 19.6 m/s².
Step 9: Divide the result from Step 7 by the result from Step 8: 400 m²/s² / 19.6 m/s² ≈ 20.41 m.
Step 10: The maximum height reached by the projectile is approximately 20.41 m.

Projectile Motion – Understanding the motion of an object thrown into the air, including the effects of gravity and launch angle.
Kinematic Equations – Applying the appropriate equations to calculate maximum height, taking into account initial velocity, angle, and gravitational acceleration.