projectile motion

JetGot

2010-07-17 10:02 pm

A boy slides down along a water slide from a height of 5m from the pool surface. When leaving the slide, he is projected horizontally. He falls into the pool which is 1m below the slife exit after travelling by a horzontal distance d. Find d.

更新1:

final answer : 4.00m

回答 (1)

六呎將軍

2010-07-17 10:31 pm

✔ 最佳答案

By energy consideration:

KE = GPE

mv2/2 = mgh

v2 = 2gh where v is the velocity of the boy when he leaves the slide

= 2 x 10 x 5 = 100

v = 10 m/s

Now, considering the vertical part of his projectile motion:

Displacement = 1 m, initial velocity = 0 m/s and acc. = 10 m/s2, we have

s = ut + at2/2

1 = 5t2

t = 0.447 s

So time of flight = 0.447 s

d = 5 x 0.447 = 2.24 m

2010-07-17 14:32:12 補充：
Correction to the last line:

d = 10 x 0.447 = 44.7 m

2010-07-17 16:24:31 補充：
Vertical height fallen when he reaches the base of the slide = 4m, so:
v^2 = 2gh = 80
v = 8.94 m/s
With time of flight = 0.447 s
d = 8.94 x 0.447 = 4.00 m

參考: Myself

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