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ScanSolve AI Tutor · Accepted 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.

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Step-by-step solution

Identify the given information.

Determine what needs to be calculated.

Recall the relevant physics formula.

Substitute the given values into the formula.

Calculate the square of the initial velocity.

Calculate the sine of the angle and square it.

Calculate the denominator.

Substitute these calculated values back into the formula for H.

Calculate the numerator.

Perform the final division to find the maximum height.

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