Question

question 24 (1 point)
when you drop a pebble from height h, it reaches the ground with kinetic energy k if there is no air resistance. from what height should you drop it so it will reach the ground with four times as much kinetic energy?
a) 8h
b) 4h
c) √2h
d) 16h
e) 2h

Explanation:

Step1: Apply conservation of mechanical energy

According to the conservation of mechanical energy, the potential energy at height \(H\) is converted into kinetic energy at the ground. So, \(K = mgH\).

Step2: Find the new height for \(4K\)

Let the new height be \(h\). Then \(4K=mg h\). Substitute \(K = mgH\) into \(4K=mg h\), we get \(4mgH=mg h\).

Step3: Solve for \(h\)

Cancel out \(mg\) from both sides of the equation \(4mgH=mg h\). We obtain \(h = 4H\).

Answer:

B. \(4H\)