Answer:
about 5.613 seconds
Step-by-step explanation:
Using the quadratic formula to find the value of t when h = 0, we have ...
at² +bt +c = 0
t = (-b±√(b²-4ac))/(2a)
t = (-72±√(72² -4(-16)(100)))/(2(-16))
t = (-72±√11584)/-32 = (9±√181)/4
Only the positive value of t is of interest.
The coin will hit the stream after (9+√181)/4 seconds ≈ 5.613 seconds.
Answer:
The height of a bouncing ball is defined by .
Step-by-step explanation:
According to this statement, we need to derive the expression of the height of a bouncing ball, that is, a function of the number of bounces. The exponential expression of the bouncing ball is of the form:
,
,
(1)
Where:
- Height reached by the ball on the first bounce, measured in feet.
- Decrease rate, no unit.
- Number of bounces, no unit.
- Height reached by the ball on the n-th bounce, measured in feet.
The decrease rate is the ratio between heights of two consecutive bounces, that is:
(2)
Where is the height reached by the ball on the second bounce, measured in feet.
If we know that and
, then the expression for the height of the bouncing ball is:
The height of a bouncing ball is defined by .