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

they start with the same

answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in   melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.