Applications Of Derivatives Question 102
Question: A ball is dropped from a platform 19.6m high. Its position function is -
Options:
A) $ x=-4.9t^{2}+19.6(0\le t\le 1) $
B) $ x=-4.9t^{2}+19.6(0\le t\le 2) $
C) $ x=-9.8t^{2}+19.6(0\le t\le 2) $
D) $ x=-4.9t^{2}-19.6(0\le t\le 2) $
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Answer:
Correct Answer: B
Solution:
[b] We have, $ a=\frac{d^{2}x}{dt^{2}}=-9.8 $
The initial conditions are $ x(0)=19.6 $ and $ v(0)=0 $ So, $ v=\frac{dx}{dt}=-9.8t+v(0)=-9.8t $
$ \therefore x=-4.9t^{2}+x(0)=-4.9t^{2}+19.6 $
Now, the domain of the function is restricted since the ball hits the ground after a certain time.
To find this time we set $ x=0 $ and solve for $ t;0=-4.9t^{2}+19.6\Rightarrow t=2 $
BETA
