How fast must a ball be thrown upward to reach a height of 12 m?
When a ball is thrown vertically upwards, there is an acceleration acting on it due to the gravitational force of attraction of the Earth equal to 9.8 m/s^2. This acts in a direction vertically downwards.
Let the magnitude of velocity required to throw the ball upwards to a height of 12 m be equal to V.
At the highest point, the velocity of the ball is equal to 0. Use the relation v^2 - u^2 = 2*a*s where v is the final velocity, u is the initial velocity, a is the acceleration and s is the distance traveled. This gives:
0^2 - V^2 = 2*(-9.8)*12
=> V^2 = 24*9.8
=> V^2 = 235.2
=> V = sqrt 235.2
=> V = 15.33
The velocity with which a ball must be thrown vertically upwards so that it reaches a height of 12 m is approximately 15.33 m/s.