Answer: a) 19.21m b) 3.92secs
Explanation:
a) Maximum height reached by the object is the height reached by an object before falling freely under gravity.
Maximum height = U²/2g
U is the initial velocity = 19.6m/s
g is acceleration due to gravity = 10m/s²
Maximum Height = 19.6²/2(10)
H = 19.21m
b) The time elapsed before the stone hits the ground is the time of flight T= 2U/g
T= 2(19.6)/10
T = 39.2/10
Time elapsed is 3.92secs
This happens in basketball. It is known as "jump ball".
Answer:
3.28 m
3.28 s
Explanation:
We can adopt a system of reference with an axis along the incline, the origin being at the position of the girl and the positive X axis going up slope.
Then we know that the ball is subject to a constant acceleration of 0.25*g (2.45 m/s^2) pointing down slope. Since the acceleration is constant we can use the equation for constant acceleration:
X(t) = X0 + V0 * t + 1/2 * a * t^2
X0 = 0
V0 = 4 m/s
a = -2.45 m/s^2 (because the acceleration is down slope)
Then:
X(t) = 4*t - 1.22*t^2
And the equation for speed is:
V(t) = V0 + a * t
V(t) = 4 - 2.45 * t
If we equate this to zero we can find the moment where it stops and begins rolling down, that will be the highest point:
0 = 4 - 2.45 * t
4 = 2.45 * t
t = 1.63 s
Replacing that time on the position equation:
X(1.63) = 4 * 1.63 - 1.22 * 1.63^2 = 3.28 m
To find the time it will take to return we equate the position equation to zero:
0 = 4 * t - 1.22 * t^2
Since this is a quadratic equation it will have to answers, one will be the moment the ball was released (t = 0), the other will eb the moment when it returns:
0 = t * (4 - 1.22*t)
t1 = 0
0 = 4 - 1.22*t2
1.22 * t2 = 4
t2 = 3.28 s
To solve this problem we will apply the concepts related to electric potential and electric potential energy. By definition we know that the electric potential is determined under the function:
= Coulomb's constant
q = Charge
r = Radius
At the same time
The values of variables are the same, then if we replace in a single equation we have this expression,
If we replace the values, we have finally that the charge is,
Therefore the potential energy of the system is 
