Answer with Explanation:
We are given that
Charge on proton,q=
a.We have to find the electric potential of the proton at the position of the electron.
We know that the electric potential
Where
B.Potential energy of electron,U=
Where
Charge on electron
=Charge on proton
Using the formula
a) 22.5 m/s
The initial vertical velocity is given by:
where
u = 35 m/s is the initial speed
is the angle of projection of the ball
Substituting into the equation, we find
b) 26.8 m/s
The initial horizontal velocity is given by:
where
u = 35 m/s is the initial speed
is the angle of projection of the ball
Substituting into the equation, we find
c) 2.30 s
The time it takes for the ball to reach the maximum heigth can be found by considering the vertical motion only. This is a uniformly accelerated motion (free-fall), so we can use the suvat equation
where
is the vertical velocity at time t
is the acceleration of gravity (negative because it is downward)
At the maximum height, the vertical velocity becomes zero, ; substituting, we find the time t at which this happens:
d) 25.8 m
The maximum height can also be found by considering the vertical motion only. We can use the following suvat equation:
where
s is the vertical displacement at time t
Substituting t = 2.30 s, we find the displacement at maximum height, so the maximum height:
e) 123.3 m
In order to find how far does the ball lands, we have to consider the horizontal motion.
First of all, the time it takes for the ball to go back to the ground is twice the time needed for reaching the maximum height:
Then, we consider the horizontal motion. There is no acceleration along this direction, so the horizontal velocity is constant:
Therefore, the horizontal distance travelled during the whole motion is
So, the ball lands 123.3 m far from the initial point.
Answer:
What is the speed of the mountain lion as it leaves the ground?
9.98m/s
At what angle does it leave the ground?
50.16°
Explanation:
This is going to be long, so if you want to see how it was solved refer to the attached solution. If you want to know the step by step process, read on.
To solve this, you will need use two kinematic equations and SOHCAHTOA:
With these formulas, we can derive formulas for everything you need:
Things you need to remember:
First we need to take your given:
10.0 m long (horizontal) and maximum height of 3.0m (vertical).
What your problem is looking for is the initial velocity and the angle it left the ground.
Vi = ? Θ =?
Vi here is the diagonal movement and do solve this, we need both the horizontal velocity and the vertical velocity.
Let's deal with the vertical components first:
We can use the second kinematic equation given to solve for the vertical initial velocity but we are missing time. So we use the first kinematic equation to derive a formula for time.
Since it is at maximum height at this point, we can assume that the lion is already making its way down so the initial vertical velocity would be 0 m/s. So we can reduce the formula:
From here we can derive the formula of time:
Now we just plug in what we know:
Now that we know the time it takes to get from the highest point to the ground. The time going up is equal to the time going down, so we can use this time to solve for the intial scenario of going up.
Remember that going up the vertical final velocity is 0m/s, and remember that gravity is always moving downwards so it is negative.
So we have our first initial vertical velocity:
Viy = 7.66m/s
Next we solve for the horizontal velocity. We use the same kinematic formula but replace it with x components. Remember that gravity has no influence horizontally so a = 0:
But horizontally, it considers the time of flight, from the time it was released and the time it hits the ground. Also, like mentioned earlier the time going up is the same as going down, so if we combine them the total time in flight will be twice the time.
T= 2t
T = 2 (0.782s)
<em>T = 1.564s</em>
<em>So we use this in our formula:</em>
<em></em>
Vix=6.39m/s
Now we have the horizontal and the vertical component, we can solve for the diagonal initial velocity, or the velocity the mountain lion leapt and the angle, by creating a right triangles, using vectors (see attached)
To get the diagonal, you just use the Pythagorean theorem:
c²=a²+b²
Using it in the context of our problem:
The lion leapt at 9.98m/s
Using SOHCAHTOA, we know that we can TOA to solve for the angle, because we have the opposite and adjacent side:
The lion leapt at an angle of 50.16°.
Answer:
Option C
Explanation:
According to the question:
Force exerted by the team towards south, F = 10 N
Force exerted by the opposite team towards North, F' = 17 N
Net Force,
Thus the force will be along the direction of force whose magnitude is higher
Therefore,
towards North