Question

On the Planet X the height of a rock thrown up is h(t) = 32t - 4t^2 meters in seconds. a. What is the equation for the velocity and acceleration of the rock? b. What is the initial velocity? c. How long will it take the rock to reach its maximum height? d. What is the max. height? e. What is the acceleration at t-=10 seconds?

Answer 1

I'm assuming this if for a calculus class?

Answer 2

If so, then

a)

Position: h(t) = 32t - 4t^2

Velocity: v(t) = h'(t) = 32 - 8t

Acceleration: a(t) = v'(t) = -8

Answer 3

b) Initial velocity is when t = 0, so

v(t) = 32 - 8t

v(0) = 32 - 8(0)

v(0) = ???

Answer 4

Yes CALC

Answer 5

v= 32

Answer 6

c)

Set the velocity function equal to zero and solve for t

v(t) = 32 - 8t

0 = 32 - 8t

32 - 8t = 0

t = ??

Answer 7

good, so the initial velocity is 32 m/s

Answer 8

Is initial velocity 0?

Answer 9

no, 32 m/s

Answer 10

OK

Answer 11

How long...?

Answer 12

d. What is the max. height?

Take the answer you get from part c) and plug it into h(t) = 32t - 4t^2

Answer 13

when 32 - 8t = 0, t = ???

Answer 14

e. What is the acceleration at t = 10 seconds

the acceleration function is a(t) = -8 and this is found in part a

this is a constant function, so it will NEVER change

the acceleration therefore is ALWAYS -8 m/s^2

Answer 15

so on this unknown planet, objects coming closer to it will speed up by 8 m/s every second they get closer to the planet

Answer 16

b. What is the initial velocity?

32 m/s (shown above)

Answer 17

Awesome! Thanks a ton!

Answer 18

How do I give you points or whatever??

Answer 19

you just did, thx