projectile motion

2010-07-16 10:24 pm

A stone is thrown upwards from the top of a cliff with an initial velocity u = 10m/s
at an elevation of 30 degree. The height of the cliff is 30m. After time t, the stone strikes the ground at point P
Find t & the velocity v of the stone at point P

回答 (1)

天同

2010-07-16 11:51 pm

✔ 最佳答案

Consider the vertical motion,
use equation of motion s = ut + (1/2)at^2
with u = 10.sin(30) m/s = 5 m/s, a = -g(=-10 m/s2),
s = -30 m, t = ?
hence, -30 = 5t + (1/2)(-10)t^2
i.e. t^2 - t - 6 = 0
t = 3 s or -2 s (rejected)

Use equation fo rmotion: v = u + at
with u = 5 m/s, a = -g, t = 3 s, v = ?
hence, v = 5 + (-10).(3) m/s = -25 m/s

Since horizontal velocity = 10.cos(30) m/s = 8.66 m/s
hence, velocity at P = square-root[8.66^2 + 25^2] m/s = 26.46 m/s

Let b be the angle at which the velocity makes with the vertical,
tan(b) = 8.66/25
i.e. b = arc-tan(8.66/25) degrees = 19.1 degrees

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