A projectile is launched at an angle of 30 degrees with an initial speed of 20 m/s. What is the maximum height it reaches? (2022)

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Q: A projectile is launched at an angle of 30 degrees with an initial speed of 20 m/s. What is the maximum height it reaches? (2022)

Solution: Using the formula: H = (u² * sin²θ) / (2g). H = (20² * (1/2)) / (2 * 9.8) = 10.2 m, approximately 10 m.

Steps: 11

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 approximately 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: H = (20² * (0.5)²) / (2 * 9.8).
Step 6: Calculate 20², which is 400.
Step 7: Calculate (0.5)², which is 0.25.
Step 8: Multiply 400 by 0.25 to get 100.
Step 9: Calculate 2 * 9.8, which is 19.6.
Step 10: Divide 100 by 19.6 to find H: H = 100 / 19.6 ≈ 5.1 m.
Step 11: Round the answer to the nearest whole number if needed. The maximum height is approximately 5 m.