Question

1. A ball is thrown vertically up with a speed of 14 m/s. 2 s later a second ball is dropped from the same point. Find when and where the two balls will meet

Answer 1

Explanation:

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1). To determine the time of intersection, subtract the two parabolic expressions to equate the result to zero. Then solve for the time (x).

(14 * x - 0.5 * 9.80665 * x^2) - (-0.5 * 9.80665 * (x - 2)^2) = 0

14 * x - 4.903325 * x^2 + 4.903325 * x^2 - (4.903325 * 4) * x + 4.903325 * 4 = 0

Eliminate the above highlighted values leaving…

(14 - 19.6133) * x = -19.6133 => -5.6133 * x = -19.6133

x = -19.6133/-5.6133 = 3.494076568150642s

2). To find the height at which the two balls intersect, substitute this time back into either parabolic expression…

14 * 3.494076568150642 - 0.5 * 9.80665 * 3.494076568150642^2

= -10.94551975876605m

The Impact Velocity of the Green Ball = 20.26519m/s

➡The Impact Velocity of the Red Ball = 14.651886m/s

Answer 2

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1). To determine the time of intersection, subtract the two parabolic expressions to equate the result to zero. Then solve for the time (x).

(14 × x - 0.5 × 9.80665 × x²) - (-0.5 × 9.80665 × (x - 2)²) = 0

14 × x - 4.903325 × x² + 4.903325 × x² - (4.903325 × 4) × x + 4.903325 × 4 = 0

Eliminate the above highlighted values leaving…

(14 - 19.6133) × x = -19.6133 => -5.6133 × x = -19.6133

x = -19.6133/-5.6133 = 3.494076568150642s

2). To find the height at which the two balls intersect, substitute this time back into either parabolic expression…

14 × 3.494076568150642 - 0.5 × 9.80665 × 3.494076568150642²

= -10.94551975876605m

The Impact Velocity of the Green Ball = 20.26519m/s

➡The Impact Velocity of the Red Ball = 14.651886m/s