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: Initial velocity (v₀) = 20 m/s Angle of projection (θ) = 30° Acceleration due to gravity (g) = 9.8 m/s² Step 2: Determine the formula for the horizontal range (R). The horizontal range of a projectile is given by the formula: R = (v₀² * sin(2θ)) / g Step 3: Substitute the given values into the formula. R = ( (20 m/s)² sin(2 30°) ) / 9.8 m/s² Step 4: Calculate the value of sin(2θ). 2 * 30° = 60° sin(60°) = √(3)/2 ≈ 0.866 Step 5: Substitute the value of sin(60°) back into the range formula. R = ( (400 m²/s²) * 0.866 ) / 9.8 m/s² Step 6: Perform the multiplication in the numerator. 400 m²/s² * 0.866 = 346.4 m²/s² Step 7: Perform the division to find the range. R = 346.4 m²/s² / 9.8 m/s² R ≈ 35.35 m The horizontal range of the projectile is approximately 35.35 meters. That's 2 down. 3 left today — send the next one.