Author Question: How do I calculate the velocity at impact in projectile motion? (Read 951 times)

j_sun

  • Sr. Member
  • ****
  • Posts: 384
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

  • Sr. Member
  • ****
  • Posts: 268
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.



Related Topics

Need homework help now?

Ask unlimited questions for free

Ask a Question

Melanie

  • Full Member
  • ***
  • Posts: 204
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.



 

Did you know?

The modern decimal position system was the invention of the Hindus (around 800 AD), involving the placing of numerals to indicate their value (units, tens, hundreds, and so on).

Did you know?

It is believed that humans initially contracted crabs from gorillas about 3 million years ago from either sleeping in gorilla nests or eating the apes.

Did you know?

Patients should never assume they are being given the appropriate drugs. They should make sure they know which drugs are being prescribed, and always double-check that the drugs received match the prescription.

Did you know?

More than one-third of adult Americans are obese. Diseases that kill the largest number of people annually, such as heart disease, cancer, diabetes, stroke, and hypertension, can be attributed to diet.

Did you know?

Medications that are definitely not safe to take when breastfeeding include radioactive drugs, antimetabolites, some cancer (chemotherapy) agents, bromocriptine, ergotamine, methotrexate, and cyclosporine.

For a complete list of videos, visit our video library