Physics:projectile motion

2012-08-25 10:52 pm

Kilauea in Hawaii is the world's most continously active voclano. Very active volcanoes characteristically eject red hot rocks and lava rather than smoke and ash. Suppose a large rock is ejected from the volcano at an angle 25degree to the horizontal. The rock will strike the squatter area at an altitude 30m below and at a horizontal distance of 2 km from its starting point.

Questions:

1.Find the speed of the rock when it is ejected from the volcano.

2.Find the speed of the rock when it strikes the squatter area.

Please show the steps.

回答 (1)

天同

2012-08-26 1:12 am

✔ 最佳答案

1. Let u be the speed of the rock at projection.
Consider the horizontal motion of the rock: 2000 = (u.cos(25)t
where t is the time of flight
i.e. t = 2000/[u.cos(25)] ------------- (1)

Consider the vertical motion, use s = ut + (1/2)gt^2
-30 = (u.sin(25))t + (1/2)gt^2
using equation (1),
-30 = (u.sin(25)).(2000/[u.cos(25)]) + (1/2).(-10).(2000/[u.cos(25)])^2
where g, the acceleration due to gravity, is taken to be 10 m/s2
Simplifying, -30 = 2000.tan(25) - 5(2000/[u.cos(25)])^2
solve for u gives u = 159 m/s

2. Horizontal speed of rock = 159.cos(25) m/s = 144 m/s
Use equation: v^2 = u^2 + 2a.s for the vertical speed
hence, v^2 = [159.sin(25)]^2 + 2.(-10).(-30)
v^2 = 5115 (m/s)^2

Therefore, speed of rock when it strikes the squatter area
= square-root[144^2 + 5115] m/s = 161 m/s

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