# What should be the initial velocity with which a rock is thrown upwards for it to rise to a maximum height of 300 m.

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The minimum speed with which a rock should be thrown upwards so that it rises to a height of 300 m has to be determined.

Assume that air resistance is negligible. If the rock has an initial speed of v m/s, the kinetic energy of the rock is (1/2)*m*v^2. At the highest point the rock is at 300 m. The kinetic energy of the rock here is 0 and the potential energy is m*g*h = m*9.8*300

Total energy is conserved in a closed system, which is the case here. This gives: (1/2)*m*v^2 = m*9.8*300

=> v^2 = 9.8*600

=> v = `sqrt 5880`

=> v = `14*sqrt 30`

=> v `~~` 76.68 m/s

The rock has to be thrown upwards with a minimum speed of 76.68 m/s if it has to reach a height of 300 m