Question

An object is dropped from a platform100 ft high. Ignoring wind resistance, what will its speed be when it reaches the ground?

Answer 1

do you have a formula to play with?

Answer 2

since gravity is the only thing accelerating it:

a = -g

but acceleration is defined as the rate of change of velocity

dv/dt = -g

when we integrate this to vind v:

v = -gt + k, but since there is no velocity at t=0, k=0

v(t) = -gt
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but how to determine when it hits the ground? we need to know its position

velocity is defined as the rate of change of position

ds/dt = -gt

integrate again

s = -1/2 gt^2 + c , when t=0 s=100 soo, c=100

s(t) = -1/2 gt^2 + 100, solve for t when s=0

0 = -1/2 gt^2 + 100

Answer 3

@amistre64
It doesn't ask for t it asks for v

@mathdumdum123
The formula you need is
\[v ^{2}=u ^{2}+2as\]

In your case
v is the final velocity
a is the acceleration = g = 32ft/s^2
s = distance = 100

Use the formula and those values to find v

Answer 4

in my approach, i find t in order to determine v at t

Answer 5

since i dont have the formulas memorized, i take a mathical approach.

Answer 6

0 = -1/2 gt^2 + 100

1/2 gt^2 = 100

t^2 = 200/g

t = sqrt(200/g)
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v = g sqrt(200/g)

v = sqrt(200g)