(a) 3.56 m/s
(b) 11 - 3.72a
(c) t = 5.9 s
(d) -11 m/s
For most of these problems, you're being asked the velocity of the rock as a function of t, while you've been given the position as a function of t. So first calculate the first derivative of the position function using the power rule.
y = 11t - 1.86t^2
y' = 11 - 3.72t
Now that you have the first derivative, it will give you the velocity as a function of t.
(a) Velocity after 2 seconds.
y' = 11 - 3.72t
y' = 11 - 3.72*2 = 11 - 7.44 = 3.56
So the velocity is 3.56 m/s
(b) Velocity after a seconds.
y' = 11 - 3.72t
y' = 11 - 3.72a
So the answer is 11 - 3.72a
(c) Use the quadratic formula to find the zeros for the position function y = 11t-1.86t^2. Roots are t = 0 and t = 5.913978495. The t = 0 is for the moment the rock was thrown, so the answer is t = 5.9 seconds.
(d) Plug in the value of t calculated for (c) into the velocity function, so:
y' = 11 - 3.72a
y' = 11 - 3.72*5.913978495
y' = 11 - 22
y' = -11
So the velocity is -11 m/s which makes sense since the total energy of the rock will remain constant, so it's coming down at the same speed as it was going up.
Answer:
33.33 %
Explanation:
given,
error last year = 63
error this year = 42
percent decrease in the error = ?
to find the percentage difference in the error formula used is
= 
= 
= 
= 33.33 %
Percentage decrease in the number of error is equal to 33.33%.
Answer:
the correct statement is the first
The law of conservation of mass indicates the same amount of carbon will be found in the reactants as in the products.
Explanation:
The law of conservation of energy establishes that the masses are not destroyed, they can only be transformed.
Therefore the mass of carbon in the reactants (CO2 and H2O) must be in the products (glucose and oxygen)
so the correct statement is the first
The law of conservation of mass indicates the same amount of carbon will be found in the reactants as in the products.
Explanation:
Below is an attachment containing the solution.
Answer:
Explanation:
Mass of the cable car, m = 5800 kg
It goes 260 m up a hill, along a slope of 
Therefore vertical elevation of the car = 
Now, when you get into the cable car, it's velocity is zero, that is, initial kinetic energy is zero (since K.E. = 
). Similarly as the car reaches the top, it halts and hence final kinetic energy is zero.
Therefore the only possible change in the cable car system is the change in it's gravitational potential energy.
Hence, total change in energy = mgh = 
where, g = acceleration due to gravity
h = height/vertical elevation
