Question

Calculus 2 - Antiderivatives

Answer 1

In part 1 what is the time you need to solve for?

Answer 2

what do you mean?

Answer 3

Oh, that doesn't ask for a number, well you know what gravity is, and you have no other forces, so that would be the accerlation.
The problem also gives you the velocity of the tomato, but the velocity also depends on the accerlation so you have to add the a(t) term in to the velocity term too.

Answer 4

The acceleration of gravity is 9.8 m/s^2 correct? And that does not depend on velocity or height, so that would be the a(t).
The velocity is given at 35m/s and so that would be v(t) if there was no acceleration. But it has to depend on a(t) also.

Answer 5

part 1

Answer 6

part 2

Answer 7

these weren't correct

Answer 8

In problems like these... use the quadratic equation (ax^2+bx^2+c) which I call the position functions, where a will be the force of gravity, b will be your initial velocity, and c will be your initial position or height.

The first derivative of the position function is the velocity function

s'(t)= v(t)

The second derivative or the position function is the acceleration function

s''(t)= a(t)

likewise the first derivative of the velocity function is the acceleration function

v'(t) = a(t)

Answer 9

yes Im sorry... the force of gravity should be half that value. that will give you the correct answers.

so s(t) = -4.9t^2+35t+16

Answer 10

v(t) wasn't correct either.

Answer 11

use the new position function I wrote to get the correct answers

Answer 12

ill redo it if you'd like?

Answer 13

that'd be great thanks

Answer 14

what is h?

Answer 15

oh plug in the 3.56 into the position function to find the height

Answer 16

.112?

Answer 17

Start from a(t) and work your way up, by integrating.

a(t) = 9.8

v(t) is the integral of acceleration, so do that, and then find the constant of integration.

Answer 18

I got

Answer 19

@cjr712 everything is correct except t=3.56 It says that's incorrect.

Answer 20

i used 35/9.8 but I rounded to 2 decimal places

Answer 21

its ok, np. thanks a lot

Answer 22

it's 3.57

Answer 23

lol i rounded wrong :P

Answer 24

thanks