An object is dropped from a height of 400ft.
(a) Find the velocity of the object as a function of time. (neglect air resistance) I think its t=400/v is that right??
(b) Use the result in (a) to find the position function.
(a) Find the velocity of the object as a function of time. (neglect air resistance) I think its t=400/v is that right??
(b) Use the result in (a) to find the position function.
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Acceleration due to gravity is approximately -32 ft /s^2 (negative because the gravitational pull is downward); this is usually given as background information in the problem or in the unit you're working on.
So, since a = -32, integrate to get v = -32t + C. The item was dropped rather than thrown or otherwise launched, so we can say its initial velocity at t=0 was 0; C = 0.
v = -32t
Integrate to find position:
y = -16 t^2 + C
y(0) = 400, so C = 400.
y = -16t^2 + 400
So, since a = -32, integrate to get v = -32t + C. The item was dropped rather than thrown or otherwise launched, so we can say its initial velocity at t=0 was 0; C = 0.
v = -32t
Integrate to find position:
y = -16 t^2 + C
y(0) = 400, so C = 400.
y = -16t^2 + 400