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1 month ago

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A 0.2-kilogram red ball is thrown horizontally at a speed of 4 meters per second from a height of 3 meters. A 0.4-kilogram green

ball is thrown horizontally from the same height at a speed of 8 meters per second. Compared to the time it takes the red ball to reach the ground, the time it takes the green ball to reach the ground is (A) four times as great (C) the same (B) twice as great (D) one-half as great

1 answer:

babunello [8.4K]1 month ago

7 0

Answer:

option (C) the same

Step-by-step explanation:

The problem states that a 0.2 kg ball is launched at a speed of 4 m/s horizontally, while a 0.4 kg green ball is also thrown horizontally at 8 m/s.

In both scenarios, there is no vertical component of velocity given.

This indicates that both balls are in free fall vertically.

According to Newton's equations of motion, we find:

$s=ut+\frac{1}{2}at^2$

where:

s = distance

a = acceleration

t = time

In this equation, mass does not influence the outcome, as the gravitational acceleration and vertical distance are identical for both.

Thus, the time it takes for each ball to hit the ground will be the same.

Consequently, the right answer is option (C) the same

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When jumping, a flea rapidly extends its legs, reaching a takeoff speed of 1.0 m/s over a distance of 0.50 mm . part a what is t

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The flea experiences an acceleration of 1,000 m/s².

Detailed explanation

This scenario involves motion with constant acceleration.

The relevant variables include the following.

$\boxed{u \ or \ v_i = initial \ velocity}$

$\boxed{u \ or \ v_t \ or \ v_i = terminal \ or \ final \ velocity}$

$\boxed{a = acceleration \ (constant)}$

$\boxed{d = distance \ travelled}$

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The flea starts from rest, so the initial velocity is zero. The question asks for the flea's acceleration during leg extension.

The equation we apply is:

$\boxed{ \ v^2 = u^2 + 2ad \ }$

a = acceleration (m/s²)
u = initial speed = 0 m/s
v = takeoff velocity = 1.0 m/s
d = displacement = 0.50 mm

First, convert 0.50 mm to meters: $\boxed{0.50 \ mm = 0.50 \times 10^{-3} \ m = 5.0 \times 10^{-4} \ m}$

Solution steps:

Rearrange the formula to isolate acceleration (a).

$\boxed{ \ v^2 = u^2 + 2ad \ }$

$\boxed{ \ v^2 - u^2 = 2ad \ }$

$\boxed{ \ 2ad = v^2 - u^2 \ }$

$\boxed{ \ a = \frac{v^2 - u^2}{2d} \ }$

Insert the given values into the rearranged equation.

$\boxed{ \ a = \frac{(1.0)^2 - (0)^2}{2(5.0 \times 10^{-4})} \ }$

$\boxed{ \ a = \frac{1}{10 \times 10^{-4}} \ }$

$\boxed{ \ a = \frac{1}{1 \times 10^{-3}} \ }$

$\boxed{ \ a = 1 \times 10^{3}\ = 1,000 \ m/s^2 \ }$

This yields the flea's acceleration as 1,000 m/s².

Additional resources

Scientific notation: brainly.com/question/7263463
Determining substance mass: brainly.com/question/4053884
Conversion into cubic units: brainly.com/question/1446243

Keywords: flea, jumping, leg extension, takeoff velocity, initial speed, displacement, acceleration, constant acceleration, unit conversion

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Answer:

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