Question

5. Kilauea in Hawaii is the world’s most continuously active volcano. Very active volcanoes characteristically eject red-hot rocks and lava rather than smoke and ash. Suppose a large rock is ejected from the volcano with a speed of 25.0 m/s and at an angle 35.0º above the horizontal. The rock strikes the side of the volcano at an altitude 20.0 m lower than its starting point.

a. Calculate the time it takes the rock to follow this path.

b. What are the magnitude and direction of the rock’s velocity at impact?

Answer 1

a.

$a=gsin35\degree$

$v=gtsin35\degree+v_0$

$d=gt^2sin35\degree/2+v_ot=20/sin35\degree$

$2.8t^2+25t-34.9=0$

$t=\frac{-25+\sqrt{625+4\cdot2.8\cdot34.9}}{5.6}=1.23$ s

b.

$v=9.8\cdot1.23sin35\degree+25=31.9$ m/s

direction: 35.0º above the horizontal