An object is dropped Physics Question
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An object is dropped Physics Question

[From: ] [author: ] [Date: 12-04-09] [Hit: ]
s(t) = 52 - 15t - 4.905t²,v(t) = -15 - 9.At impact,4.Time of impact = t = [-15 + √(15² + 4*52*4.......
An object is hurled downward with an initial velocity of 15 m/s from a height of 52 m.

How long does the object take to hit the ground?
What speed does the object strike?

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With gravitational acceleration equal 9.81 m/s²

s(t) = 52 - 15t - 4.905t², t ≥ 0
v(t) = -15 - 9.81t

At impact, s(t) = 0
4.905t² + 15 t - 52 = 0
Time of impact = t = [-15 + √(15² + 4*52*4.905)]/9.81 = 2.07 seconds (the negative solution of the quadratic equation is discarded since the time domain doesn't include negative values of t)

Speed at impact = v(2.07) = -15 - 9.81*2.07 = -35.3 m/s (negative sign indicates the direction of the velocity vector is downward)

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d = v0 * t + (1/2)a t^2.

Plug in the known values of d, v0 and a, and solve the quadratic equation for t.

v = v0 + at.

Plug in the known values of v0, a and t.

Or use this one: v^2 = v0^2 + 2ad with the known values of v0, a and d. You could then use that value of v in v = v0 + at to find t.
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