Forces always come in pairs — so each _____

In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy without the aid of a pole.

Fiesta28 [93]

Answer:

6.0 m/s

Explanation:

According to the law of conservation of energy, the total mechanical energy (potential, PE, + kinetic, KE) of the athlete must be conserved.

Therefore, we can write:

$KE_i+PE_i =KE_f+PE_f$

or

$\frac{1}{2}mu^2+0=\frac{1}{2}mv^2+mgh$

where:

m is the mass of the athlete

u is the initial speed of the athlete (at the bottom)

0 is the initial potential energy of the athlete (at the bottom)

v = 0.80 m/s is the final speed of the athlete (at the top)

$g=9.8 m/s^2$ is the acceleration due to gravity

h = 1.80 m is the final height of the athlete (at the top)

Solving the equation for u, we find the initial speed at which the athlete must jump:

$u=\sqrt{v^2+2gh}=\sqrt{0.80^2+2(9.8)(1.80)}=6.0 m/s$

4 0

3 years ago

A ball is dropped from a building taking 3sec to fall to the ground. Calculate:

GenaCL600 [577]

Answer:

Vf = 29.4 m/s

h = 44.1 m

Explanation:

Data:

Initial Velocity (Vo) = 0 m/s
Gravity (g) = 9.8 m/s²
Time (t) = 3 s
Final Velocity (Vf) = ?
Height (h) = ?

==================================================================

Final Velocity

Use formula:

Vf = g * t

Replace:

Vf = 9.8 m/s² * 3s

Multiply:

Vf = 29.4 m/s

==================================================================

Height

Use formula:

$\boxed{h=\frac{g*(t)^{2}}{2}}$

Replace:

$\boxed{h=\frac{9.8\frac{m}{s^{2}}*(3s)^{2}}{2}}$

Multiply time squared:

$\boxed{h=\frac{9.8\frac{m}{s^{2}}*9s^{2}}{2}}$

Simplify the s², and multiply in the numerator:

$\boxed{h=\frac{88.2m}{2}}$

It divides:

$\boxed{h=44.1\ m}$

What is the velocity when falling to the ground?

The final velocity is 29.4 meters per seconds.

How high is the building?

The height of the building is 44.1 meters.

3 0

3 years ago

Find a parametric representation for the surface. The plane through the origin that contains the vectors i - j and j - k

boyakko [2]

Answer:

parametric representation: x = u, y = v - u , z = - v

Explanation:

Given vectors :

i - j , j - k

represent the vector equation of the plane as:

r ( u, v ) = r₀ + ua + vb

where: r₀ = position vector

u and v = real numbers

a and b = nonparallel vectors

expressing the nonparallel vectors as :

a = i -j , b = j - k , r = ( x,y,z ) and r₀ = ( x₀, y₀, z₀ )

hence we can express vector equation of the plane as

r(u,v) = ( x₀ + u, y₀ - u + v, z₀ - v )

Finally the parametric representation of the surface through (0,0,0) i.e. origin = 0

( x, y , z ) = ( x₀ + u, y₀ - u + v, z₀ - v )

x = 0 + u ,

y = 0 - u + v

z = 0 - v

∴ parametric representation: x = u, y = v - u , z = - v

3 0

3 years ago

20 cubic inches of a gas with an absolute pressure of 5 psi is compressed until its pressure reaches 10 psi. What's the new volu

Anna71 [15]

Answer:

B. $V_{f}= 10\,cubic\,inches$

Explanation:

Assuming we are dealing with a perfect gas, we should use the perfect gas equation:

$PV=nRT$

With T the temperature, V the volume, P the pressure, R the perfect gas constant and n the number of mol, we are going to use the subscripts i for the initial state when the gas has 20 cubic inches of volume and absolute pressure of 5 psi, and final state when the gas reaches 10 psi, so we have two equations:

$P_{i}V_{i}=n_{i}RT_{i}$ (1)

$P_{f}V_{f}=n_{f}RT_{f}$ (2)

Assuming the temperature and the number of moles remain constant (number of moles remain constant if we don't have a leak of gas) we should equate equations (1) and (2) because $T_{i}=T_{f}$ , $n_{i}=n_{f}$ and R is an universal constant:

$P_{i}V_{i}= P_{f}V_{f}$ , solving for $V_{f}$

$V_{f} =\frac{P_{i}V_{i}}{P_{f}} =\frac{(5)(20)}{10}$

$V_{f}= 10 cubic\,inches$

6 0

3 years ago

A 73.0 kg firefighter climbs a flight of stairs 9.0 m high. how much work is required? j

pshichka [43]

The strength of the fireman in vertical direction will be given by F = m * g. Then, the work done will be given by definition by W = F * d. Substituting the expression of the Force in that of the work, we have that the work will be W = m * g * d. Substituting the given values and assuming that g = 10m / s ^ 2, we have a total work of W = (73) * (10) * (9) = 6570 J

7 0

3 years ago

Forces always come in pairs — so each ______ has a reaction