This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given information. The problem provides the following values: Initial velocity (v₀) = 15 m/s Angle (θ) = 30° Acceleration due to gravity (g) = 9.8 m/s² Step 2: Determine what needs to be calculated. The question asks for the maximum height reached by the projectile. Step 3: Recall the relevant physics formula. The formula for the maximum height (H) of a projectile is: H = (v₀² sin²(θ)) / (2 g) Step 4: Substitute the given values into the formula. H = (15 m/s)² sin²(30°) / (2 9.8 m/s²) Step 5: Calculate the square of the initial velocity. 15² = 225 m²/s² Step 6: Calculate the sine of the angle and square it. sin(30°) = 0.5 sin²(30°) = (0.5)² = 0.25 Step 7: Calculate the denominator. 2 * 9.8 m/s² = 19.6 m/s² Step 8: Substitute these calculated values back into the formula for H. H = (225 m²/s² * 0.25) / (19.6 m/s²) Step 9: Calculate the numerator. 225 * 0.25 = 56.25 m²/s² Step 10: Perform the final division to find the maximum height. H = 56.25 m²/s² / 19.6 m/s² H ≈ 2.87 m The maximum height reached by the projectile is approximately 2.87 meters.