Question

A projectile is fired straight upward with a velocity of 400 ft/sec. From physics, it's the distance above the ground after "t" seconds, given by s(t)=-16t^2 + 400t.

a) What is the time elapsed when the projectile hits the ground?
b) What is the "impact" velocity/
c) What is the maximum altitude achieved by the projectile?
d) What is the acceleration at anytime "t"?

Answer 1

we can use calculus, right?

Answer 2

Yes

Answer 3

first off what is s(t)=?
when the projectile hits the ground

Answer 4

?

Answer 5

Well that was how the question was given to me...

Answer 6

right, so I'm asking you:
if s(t) represents the height of the ball, then what is s(t) when the ball hits the ground? Just use logic.

Answer 7

0?

Answer 8

sure! that's what "on the ground" means, right?
so you need to solve\[s(t)=-16t^2+400t=0\] that is step one

Answer 9

Okay cool so I get 25 sec

Answer 10

For a

Answer 11

right, now we need a formula for velocity
hopefully you already know that
v(t)=s'(t)
so we need to take the derivative of s(t) and plug in t=25 into v(t) to get the impact velocity. Make sense?

Answer 12

Yes, I understand, thank you, now I'm a little confused on c.

Answer 13

But I understand d

Answer 14

there are a few ways to see this...
from a physics perspective, at the maximum height the velocity is zero, so we need to solve
v(t)=0

from a calculus perspective we can use max/min techniques to find the maximum of s(t), which means setting s'(t)=0, which is the same thing.

so physics and math are consistent, hooray!

Answer 15

back in 5min if you have more questions...

Answer 16

Okay thank you so much.

Answer 17

ok a little preoccupied, I have to go again but do you have any quick questions?

Answer 18

Um can you help differentiate
y=2^3x

Answer 19

this is a tolatally different problem, yes?

Answer 20

totally*

Answer 21

Yes, haha. sorry, you can go if your busy

Answer 22

yeah five me another five or ten
if you mean \[2^{3x}\]try to apply\[{d \over dx}(a^x)=a^x \ln a\]plus the chain rule \[f[(g(x)]'=f'[g(x)]g'(x)\] and see what you get. good luck!

Answer 23

Thank you!