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3 years ago

14

Use the Pythagorean theorem to answer the following question. A ping-pong ball is shot straight north from a popgun at 4.0 m/s.

The wind is blowing to the west at 3.0 m/s. What is the actual velocity of the ping-pong ball?

2 answers:

dybincka [34]3 years ago

5 0

Answer : The actual velocity of the ping-pong ball is, 5 m/s

Explanation :

Using Pythagorean theorem :

$(Hypotenuse)^2=(Base)^2+(Perpendicular)^2$

The diagram is shown below.

From the diagram we conclude that,

AB = 4 m/s

BC = 3 m/s

AC = ?

$(AC)^2=(BC)^2+(AB)^2$

Now put all the given values in this formula, we get

$(AC)^2=(3)^2+(4)^2$

$AC=5m/s$

Therefore, the actual velocity of the ping-pong ball is, 5 m/s

MaRussiya [10]3 years ago

4 0

Resultant is 5 m/s using the Pythagorean theorem<span />

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Two 51 g blocks are held 30 cm above a table. As shown in the figure, one of them is just touching a 30-long spring. The blocks

vivado [14]

The concept of this question can be well understood by listing out the parameters given.

The mass of the block = 51 g = 51 × 10⁻³ kg
The distance of the block from the table = 30 cm
Length of the spring = 30 cm

The purpose is to determine the spring constant.

Let us assume that the two blocks are Block A and Block B.

At point A on block A, the initial velocity on the block is zero

i.e. u = 0

We want to determine the time it requires for Block A to reach the table. The can be achieved by using the second equation of motion which can be expressed by using the formula.

$\mathsf{S = ut + \dfrac{1}{2}gt^2}$

From the above formula,

The distance (S) = 30 cm; we need to convert the unit to meter (m).

Since 1 cm = 0.01 m
Then, 30cm = 0.3 m

The acceleration (g) due to gravity = 9.8 m/s²

∴

inputting the values into the equation above, we have;

$\mathsf{0.3 = (0)t + \dfrac{1}{2}*(9.80)*(t^2)}$

$\mathsf{0.3 = \dfrac{1}{2}*(9.80)*(t^2)}$

$\mathsf{0.3 =4.9*(t^2)}$

By dividing both sides by 4.9, we have:

$\mathsf{t^2 = \dfrac{0.3}{4.9}}$

$\mathsf{t^2 = 0.0612}$

$\mathsf{t = \sqrt{0.0612}}$

$\mathsf{t =0.247 \ seconds}$

However, block B comes to an instantaneous rest on point C. This is achieved by the dropping of the block on the spring. During this process, the spring is compressed and it bounces back to oscillate in that manner. The required time needed to get to this point C is half the period, this will eventually lead to the bouncing back of the block with another half of the period, thereby completing a movement of one period.

By applying the equation of the time period of a simple harmonic motion.

$\mathsf{T = 2 \pi \sqrt{\dfrac{m}{k}}}$

where the relation between time (t) and period (T) is:

$\mathsf{t = \dfrac{T}{2}}$

T = 2t

T = 2(0.247)

T = 0.494 seconds

$\mathsf{T = 2 \pi \sqrt{\dfrac{m}{k}}}$

By making the spring constant k the subject of the formula:

$\mathsf{\dfrac{T}{2 \pi } = \sqrt{ \dfrac{m}{k}}}$

$\Big(\dfrac{T}{2 \pi }\Big)^2 = { \dfrac{m}{k}$

$\dfrac{T^2}{(2 \pi)^2 }= { \dfrac{m}{k}$

$\mathsf{ T^2 *k = 2 \pi^2*m} \\ \\ \mathsf{ k = \dfrac{2 \pi^2*m}{T^2}}$

$\mathsf{ k =\Big( \dfrac{(2 \pi)^2*(51 \times 10^{-3})}{(0.494)^2} \Big) N/m}$

$\mathbf{ k =8.25 \ N/m}$

Therefore, we conclude that the spring constant as a result of instantaneous rest caused by the compression of the spring is 8.25 N/m.

Learn more about simple harmonic motion here:

brainly.com/question/17315536?referrer=searchResults

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3 years ago

Very large forces are produced in joints when a person jumps from some height to the ground. Calculate the force produced if an

krok68 [10]

Answer:

A) 31 kJ

B) 1.92 KJ

C) 40 , 2.48

Explanation:

weight of person ( m ) = 79 kg

height of jump ( h ) = 0.510 m

Compression of joint material ( d ) = 1.30 cm ≈ 0.013 m

A) calculate the force

Fd = mgh

F = mgh / d

W = mg

F(net) = W + F = mg ( 1 + $\frac{h}{d} )$

= 79 * 9.81 ( 1 + (0.51 / 0.013) )

= 774.99 ( 40.231 ) ≈ 31 KJ

B) calculate the force when the stopping distance = 0.345 m

d = 0.345 m

Fd = mgh hence F = mgh / d

F(net) = W + F = mg ( 1 + $\frac{h}{d} )$

= 79 * 9.81 ( 1 + (0.51 / 0.345) )

= 774.99 ( 2.478 ) = 1.92 KJ

C) Ratio of force in part a with weight of person

= 31000 / ( 79 * 9.81 ) = 31000 / 774.99 = 40

Ratio of force in part b with weight of person

= 1920 / 774.99 = 2.48

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Unlike a longitudinal wave, a transverse wave moves about, perpendicular to the direction of propagation. The particles in a transverse wave do not travel along the direction of propagation, but only oscillate up and down on its equilibrium position. With this, the displacement can be determined by measuring (in the case of electronic waves, using an oscilloscope or spectrum analyzer) and setting the desired units to measure the wave in.

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Gala2k [10]

The electric field between the plates is equal to the potential difference across the plates divided by the separation of the plates.
The potential difference across the plates is equal to the charge stored divided by the capacitance.

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patriot [66]

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