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3 years ago

Ingrid kicks a football with an initial velocity at 12 m/s at an angle of 45 relative to the ground

1 answer:

5 0

Equation of movement is

y(x) = x * tg (a) - $\frac{g}{2 * u^{2} * cos (a)^{2} } * x^{2}$

where y is y-coordinate, x - x coordinate, u - your initial speed, a = angle above horizon.

differentiate it to get dy/dx (speed)

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skateboarder, starting from rest, rolls down a 13.5 m ramp. When she arrives at the bottom of the ramp her speed is 7.37 m/s. If

scZoUnD [109]

Answer:

1.7 m/s²

Explanation:

d = length of the ramp = 13.5 m

v₀ = initial speed of the skateboarder = 0 m/s

v = final speed of the skateboarder = 7.37 m/s

a = acceleration

Using the equation

v² = v₀² + 2 a d

7.37² = 0² + 2 a (13.5)

a = 2.01 m/s²

θ = angle of the incline relative to ground = 29.9

a' = Component of acceleration parallel to the ground

Component of acceleration parallel to the ground is given as

a' = a Cosθ

a' = 2.01 Cos29.9

a' = 1.7 m/s²

7 0

3 years ago

Calculate the height of a cliff if it takes 2.35s for a rock to hit the ground when it is thrown straight up from the cliff with

ad-work [718]

Answer:

y₀ = 10.625 m

Explanation:

For this exercise we will use the kinematic relations, where the upward direction is positive.

y = y₀ + v₀ t - ½ g t²

in the exercise they indicate the initial velocity v₀ = 8 m / s.

when the rock reaches the ground its height is zero

0 = y₀ + v₀ t - ½ g t²

y₀i = -v₀ t + ½ g t²

let's calculate

y₀ = - 8 2.5 + ½ 9.8 2.5²

y₀ = 10.625 m

7 0

2 years ago

A certain parallel-plate capacitor is filled with a dielectric for which Κ = 5.5 .The area of each plate is 0.034 m2 , and the p

Nesterboy [21]

Answer:

The maximum energy that can be stored in the capacitor is 6.62 x 10⁻⁵ J

Explanation:

Given that,

dielectric constant k = 5.5

the area of each plate, A = 0.034 m²

separating distance, d = 2.0 mm = 2 x 10⁻³ m

magnitude of the electric field = 200 kN/C

Capacitance of the capacitor is calculated as follows;

$C = \frac{k \epsilon A}{d} = \frac{5.5*8.85*10^{-12}*0.034}{2*10^{-3}} = 8.275 *10^{-10} \ F$

Maximum potential difference:

V = E x d

V = 200000 x 2 x 10⁻³ = 400 V

Maximum energy that can be stored in the capacitor:

E = ¹/₂CV²

E = ¹/₂ x 8.275 x 10⁻¹⁰ x (400)²

E = 6.62 x 10⁻⁵ J

Therefore, the maximum energy that can be stored in the capacitor is 6.62 x 10⁻⁵ J

4 0

3 years ago

A 24 cm radius aluminum ball is immersed in water. Calculate the thrust you suffer and the force. Knowing that the density of al

Illusion [34]

Answer:

W =1562.53 N

Explanation:

It is given that,

Radius of the aluminium ball, r = 24 cm = 0.24 m

The density of Aluminium, $d=2698.4\ kg/m^3$

We need to find the thrust and the force. The mass of the liquid displaced is given by :

$m=dV$

V is volume

Weight of the displaced liquid

W = mg

$W=dVg$

So,

$W=dg\times \dfrac{4}{3}\pi r^3\\\\W=2698.4\times 10\times \dfrac{4}{3}\times \pi \times (0.24)^3\\\\W=1562.53\ N$

So, the thrust and the force is 1562.53 N.

7 0

2 years ago

A 87.0 kg astronaut is working on the engines of a spaceship that is drifting through space with a constant velocity. The astron

Ket [755]

Answer:

259.62521 seconds

Explanation:

$m_1$ = Mass of astronaut = 87 kg

$m_2$ = Mass of wrench = 0.57 kg

$v_1$ = Velocity of astronaut

$v_2$ = Velocity of wrench = 22.4 m/s

Here, the linear momentum is conserved

$m_1v_1=m_2v_2\\\Rightarrow v_1=\frac{m_2v_2}{m_1}\\\Rightarrow v_1=\frac{0.57\times 22.4}{87}\\\Rightarrow v_1=0.14675\ m/s$

Time = Distance / Speed

$Time=\frac{38.1}{0.14675}=259.62521\ s$

The time taken to reach the ship is 259.62521 seconds

4 0

3 years ago