(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.
Current is defined as the rate of charge flowing a point every second. Having a current of 1 Ampere signifies 1 Coulomb is flowing in a circuit every second. It is measured by the use of an ammeter which is positioned in series to the component to be measured. The current in the problem is calculated as follows:
I = 2.0 x 10^-4 C / 5.0 x 10^-5 s
<span>I = 4 A or 4.0 x 10^0 A</span>
Answer:
The velocity of the ball when its hit the ground will be 54.22 m/sec
Explanation:
We have given height from which ball is dropped h = 150 m
Acceleration due to gravity 
As the ball is dropped so initial velocity will be zero so u = 0 m/sec
According to third equation of motion we know that 
So the velocity of the ball when its hit the ground will be 54.22 m/sec
<h2>
Answer:</h2>
Workdone = 601.33 Nm
<h2>
Explanation:</h2>
Workdone = Force(F) x horizontal distance(d).
Wordone = F x d
Where F is the horizontal component of the force
Force = 35 pounds
Recall that;
1 pound force = 4.4N
=> 35 pounds = 35 x 4.4N = 154N
=> Force = 154N
But since the rope makes a 10⁰ angle with the ground,
The horizontal component of the force F is Force x cos10⁰
=> F = 154 cos 10⁰
=> F = 154 x 0.9848
=> F = 151.66N
Horizontal distance (d) = 13 feet
Recall that;
1 foot = 0.305m
=> 13 feet = 13 x 0.305m = 3.965m
=> d = 3.965m
=> Substituting the values of F and d into the equation above, we have;
Workdone = F x d
Workdone = 151.66N x 3.965m
Workdone = 601.33Nm
