When a ball is thrown up vertically with velocity V_0, it reaches a maximum height of h. If one wishes to triple the maximum height then the ball should be thrown with velocity:a. √(3) V_0b. 3 V_0c. 9 V_0d. 3 / 2 V_0
Question
When a ball is thrown up vertically with velocity V_0, it reaches a maximum height of h. If one wishes to triple the maximum height then the ball should be thrown with velocity:a. √(3) V_0b. 3 V_0c. 9 V_0d. 3 / 2 V_0
Solution
The maximum height (h) reached by a ball thrown vertically is given by the equation h = V_0^2 / (2g), where V_0 is the initial velocity and g is the acceleration due to gravity.
If we want to triple the maximum height (3h), we can set up the equation 3h = V_1^2 / (2g), where V_1 is the new initial velocity we're trying to find.
Substituting the first equation into the second gives us 3(V_0^2 / (2g)) = V_1^2 / (2g).
Solving for V_1, we get V_1 = sqrt(3) * V_0.
So, the ball should be thrown with a velocity of sqrt(3) * V_0 to triple the maximum height. Therefore, the answer is a. √(3) V_0.
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