A carbonate. Hope this helps!
At its maximum height h, the football has zero vertical velocity, so if it was kicked with initial upward speed v, then
0² - v² = -2gh
Solve this for v :
v² = 2gh
v = √(2gh)
The height y of the football t seconds after being kicked is
y = vt - 1/2 gt²
Substitute v = √(2gh), replace y = h, and solve for h when t = 3.8 s :
h = √(2gh) t - 1/2 gt²
h = √(2gh) (3.8 s) - 1/2 g (3.8 s)²
h ≈ (16.8233 √m) √h - 70.756 m
(By √m, I mean "square root meters"; on its own this quantity doesn't make much physical sense, but we need this to be consistent with √h. h is measured in meters, so √h is measured in √m, too.)
h - (16.8233 √m) √h + 70.756 m = 0
Use the quadratic formula to solve for √h :
√h = ((16.8233 √m) ± √((16.8233 √m)² - 4 (70.756 m))) / 2
Both the positive and negative square roots result in the same solution,
√h ≈ 8.411 √m
Take the square of both sides to solve for h itself:
(√h)² ≈ (8.411 √m)²
⇒ h ≈ 70.756 m ≈ 71 m
Answer: 1.124 m
Explanation:
This situation is a good example of the projectile motion or parabolic motion, and the main equations that will be helpful in this situations are:
x-component:
(1)
Where:
is the initial speed
is the angle at which the venom was shot
is the time since the venom is shot until it hits the ground
y-component:
(2)
Where:
is the initial height of the venom
is the final height of the venom (when it finally hits the ground)
is the acceleration due gravity
Knowing this, let's begin:
First we have to find from (2):
(3)
Rearranging (3):
(4)
This is a <u>quadratic equation</u> (also called equation of the second degree) of the form , which can be solved with the following formula:
(5)
Where:
Substituting the known values:
(6)
Solving (6) we find the positive result is:
(7)
Substituting (7) in (1):
(8)
Finally:
(9)
Answer:
The induced voltage is
Explanation:
From the question we are told that
The number of turns is
The diameter is
The initial magnetic field is
The final magnetic field is
The time taken is
The radius is mathematically evaluated as
substituting values
Generally the induced emf is mathematically represented as
Where is the change in magnetic flux of the wire which is mathematically represented as
=>
Here
since the axis of the coil is parallel to the field
Where A is the cross-sectional area of the coil which is mathematically represented as
So the induced emf
Here we substituted the values of