A ball is thrown vertically upward with an initial speed v and reaches a maximum height y1. The same ball is thrown with an initial speed 3v to reach the maximum height y2. What is the correct relationship between y2 and y1?

y2 = 9y1

Explanation:

According to projectile, the formula for calculating maximum height is expressed as;

Maximum height H = u²/2g

If a ball is thrown vertically upward with an initial speed v and reaches a maximum height y1, then

y1 = v²/2g

2g = v²/y1 1

If the same ball is thrown with an initial speed 3v to reach the maximum height y2, hence;

y2 = (3v)²/2g

2g = 9v²/y2 2

Equate 1 and 2

v²/y1 = 9v²/y2

1/y1 = 9/y2

Cross multiply

9y1 = y2

Rearrange

y2 = 9y1

Hence the correct relationship between y2 and y1 is y2 = 9y1

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