Final answer:
When you throw a pebble straight up with an initial speed V, it reaches a maximum height H. If you throw the same pebble straight up with an initial speed of 2V, it will reach a maximum height 2H.
Step-by-step explanation:
When a pebble is thrown straight up with an initial speed V, it reaches a maximum height H. If the same pebble is thrown straight up with an initial speed of 2V, the maximum height it will reach can be determined by considering the relationship between initial velocity and maximum height. The maximum height of a projectile depends only on the vertical component of the initial velocity, which is given by the equation h = (V^2)/(2g), where g is the acceleration due to gravity.
By plugging in the value of 2V for V into the equation, we get h = (4V^2)/(2g), which simplifies to h = 2H. Therefore, the pebble thrown with an initial speed of 2V will reach a maximum height 2 times greater than H, or 2H.
Therefore, the correct answer is B. 2H.