Question

(from my calculus quiz) An object is dropped and hits the ground 3 second(s) later. From what height, in feet, was it dropped? I just need an answer so I can solve it tmr on my own thanks!

Answer 1

This is free-fall kinematics. Assuming it's near Earth, the gravitational acceleration is -9.81 m/s/s (or since it's asking for feet, 32.2 ft/s/s).
you can integrate the acceleration to get velocity and integrate velocity to get position.

Answer 2

integrate ?

Answer 3

You said it's for a calculus quiz; have you studied antiderivatives and integrals yet?

Answer 4

no we are only as far as implicit d. and derivatives

Answer 5

chain rule, prod rule, quo rule etc.

Answer 6

Then just use the fundamental kinematics equation:
\[y=y_0+v_0t+\frac{1}{2}at^2\]

Answer 7

You'll be solving for y_o, the initial height. y_final = 0 since it hit the ground. v_0 = 0 because it was simply dropped and not thrown with an initial velocity, and a = -32.2ft/s/s.
Plug in t=3s and you're good to go.
Reduces to an algebra 1 problem rather quickly.

Answer 8

With only one significant figure in that given value of 3 seconds, the initial height is approximately 100 ft. You can add more precision if you like.