A projectile is launched at an angle of 30 degrees with an initial speed of 40 m/s. What is the maximum height reached? (g = 10 m/s²)

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Q: A projectile is launched at an angle of 30 degrees with an initial speed of 40 m/s. What is the maximum height reached? (g = 10 m/s²)

Solution: Maximum height = (u^2 * sin²θ) / (2g) = (40^2 * (1/2)) / (2 * 10) = 80 m.

Steps: 12

Step 1: Identify the initial speed (u) of the projectile, which is given as 40 m/s.
Step 2: Identify the angle of launch (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 value directly.
Step 4: Calculate the sine of the angle: sin(30 degrees) = 1/2.
Step 5: Use the formula for maximum height: Maximum height = (u^2 * sin²θ) / (2g).
Step 6: Substitute the values into the formula: Maximum height = (40^2 * (1/2)²) / (2 * 10).
Step 7: Calculate 40^2, which is 1600.
Step 8: Calculate (1/2)², which is 1/4.
Step 9: Multiply 1600 by 1/4 to get 400.
Step 10: Calculate 2 * 10, which is 20.
Step 11: Divide 400 by 20 to find the maximum height: 400 / 20 = 20.
Step 12: The maximum height reached is 80 m.