Author Question: How do I calculate the velocity at impact in projectile motion? (Read 1018 times)

j_sun

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For example, my position function is s(t) = -16t^2 + 96t

My velocity function is s'(t) = -32t^2+96

Can someone show me please?

Also, does the unit of measurement change after I take the derivative? Thanks!



Sandstorm

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Your second line has an error. s' = -32t + 96.

Solve s = -16t^2 + 96t = 0 to find the time of impact. (Obviously not the t = 0 solution.)

Substitute this value of t into the velocity function.

Units of velocity are distance/time e.g. ft/sec.



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Melanie

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s(t) = -16t^2 + 96t

Find the time when the object lands on the ground. It lands on the ground when s = 0.

0 = -16t^2 + 96t

0 = t(-16t + 96)

t = 0

or

-16t + 96 = 0

t = 6

============
s = -16t^2 + 96t

v = -32t + 96

v(6) = -32(6) + 96 = -96

So the velocity at impact is 96.

Note that velocity is negative because the object is falling down.

Remember that velocity represents direction AND speed.



 

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