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 = 9.8 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 = 9.8 m/s²)

Solution: The vertical component of the velocity is 40 * sin(30) = 20 m/s. Using h = (v²)/(2g), we get h = (20²)/(2 * 9.8) ≈ 20.41 m.

Steps: 11

Step 1: Identify the initial speed of the projectile, which is 40 m/s.
Step 2: Identify the launch angle, which is 30 degrees.
Step 3: Calculate the vertical component of the initial velocity using the formula: vertical velocity = initial speed * sin(angle).
Step 4: Substitute the values: vertical velocity = 40 m/s * sin(30 degrees).
Step 5: Calculate sin(30 degrees), which is 0.5.
Step 6: Now calculate the vertical velocity: vertical velocity = 40 m/s * 0.5 = 20 m/s.
Step 7: Use the formula for maximum height: h = (vertical velocity²) / (2 * g), where g = 9.8 m/s².
Step 8: Substitute the values into the formula: h = (20 m/s)² / (2 * 9.8 m/s²).
Step 9: Calculate (20 m/s)², which is 400 m²/s².
Step 10: Calculate 2 * 9.8 m/s², which is 19.6 m/s².
Step 11: Now divide 400 m²/s² by 19.6 m/s² to find h: h ≈ 20.41 m.