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The velocity when function p(t)=11 is 8 .
According to the question
The position of a car at time t represented by function :
Now,
When function p(t) = 11 , t will be
11 = t²+2t-4
0 = t² + 2t - 15
or
t² +2t-15 = 0
t² +(5-3)t-15 = 0
t² +5t-3t-15 = 0
t(t+5)-3(t+5) = 0
(t-3)(t+5) = 0
t = 3 , -5
as t cannot be -ve as given ( t≥0)
so,
t = 3
Now,
the velocity when p(t)=11
As we know velocity =
therefore to get the value of velocity from function p(t)
we have to differentiate the function with respect to time
v(t) = 2t + 2
where v(t) = velocity at that time
as t = 3 for p(t)=11
so ,
v(t) = 2t + 2
v(t) = 2*3 + 2
v(t) = 8
Hence, the velocity when function p(t)=11 is 8 .
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Answer:
a)
b) Ball 1 has a greater speed than ball 2 when they are passing.
c) The height is the same for both balls = 3h/4.
Explanation:
a) We can find the time when the two balls meet by equating the distances as follows:
Where:
: is the initial height = h
: is the initial speed of ball 1 = 0 (it is dropped from rest)
(1)
Now, for ball 2 we have:
Where:
: is the initial height of ball 2 = 0
(2)
By equating equation (1) and (2) we have:
Where the initial velocity of the ball 2 is:
Since = 0 at the maximum height (h):
Hence, the time when they pass each other is:
b) When they are passing the speed of each one is:
For ball 1:
The minus sign is because ball 1 is going down.
For ball 2:
Therefore, taking the magnitude of ball 1 we can see that it has a greater speed than ball 2 when they are passing.
c) The height of the ball is:
For ball 1:
For ball 2:
Then, when they are passing the height is the same for both = 3h/4.
I hope it helps you!