Question

When you throw a pebble straight up with initial speed V, it reaches a maximum height H with no air resistance. At what speed should you throw it up vertically so it will go twice as high? 16 V 8 V 4V 2V squareroot 2V

Answer 1

`√(2)V`

Step-by-step explanation:

Velocity at maximum height is 0 m/s. With initial velocity, V, height h and acceleration of gravity, g,

`v_f^2 = v_i^2+2as`

`0^2 = V^2 -2gh`

g is negative because the motion is against gravity.

`V = √(2gh)`

If the maximum height were doubled, then we have

`V_1=√(2g*2h) = √(2)√(2gh) = √(2)V`