A rock is at the top of a 20 meter tall hill. The rock has a mass of 10kg. How much potential energy does it have?

Answer:

(a) t = 4.52 sec

(b) X = 1,156.49 m

Explanation:

Horizontal Launching

If an object is launched horizontally, its initial speed is zero in the y-coordinate and the horizontal component of the velocity remains the same in time. The distance x is computed as.

(a)

The vertical component of the velocity starts from zero and gradually starts to increase due to the acceleration of gravity as follows

This means the vertical height is computed by

Where is the initial height. Our fighter bomber is 100 m high, so we can compute the time the bomb needs to reach the ground by solving the above equation for t knowing h=0

(b)

We now compute the horizontal distance knowing

Answer:

C

Explanation:

To melt the alcohol

Heat needed = M . L  = 2 . 25  = 50 kcal

To warm up the alcohol

Heat needed = M . sp. ht. . ∆t   = 2 . 0.6 . 100  = 120 kcal

Total heat needed = 170 kcal

Assuming that 0.6 kcal/ kg / ˚C  is the specific heat and that the answer is wanted in kcal ( a rather odd unit to be in use here.)

The numbers in power of 10 notation would be :

3 trillion is expressed as 3 ×  10¹².

Five-thousandths (0.005) are expressed as 5 × 10⁻³.

730,000,000,000,000 is expressed as 7.3 × 10¹⁴.

0.000000000082 is expressed as 8.2 × 10⁻¹¹.

3 trillion:

In standard form: 3,000,000,000,000

In powers of 10 notation: 3 × 10¹²

Explanation: In this number, 3 is multiplied by 10 raised to the power of 12, indicating that it is 3 followed by 12 zeros. This notation is particularly useful when dealing with very large numbers like the national debt or astronomical distances.

Five-thousandths (0.005):

In standard form: 0.005

In powers of 10 notation: 5 × 10⁻³

Explanation: Here, 5 is multiplied by 10 raised to the power of -3, indicating that it is 5 divided by 1,000 (10³). This notation helps represent fractions or very small quantities.

730,000,000,000,000:

In standard form: 730,000,000,000,000

In powers of 10 notation: 7.3 × 10¹⁴

Explanation: In this case, 7.3 is multiplied by 10 raised to the power of 14, indicating that it is 7.3 followed by 14 zeros. This notation simplifies the expression of extremely large numerical values.

0.000000000082:

In standard form: 0.000000000082

In powers of 10 notation: 8.2 × 10⁻¹¹

Explanation: Here, 8.2 is multiplied by 10 raised to the power of -11, indicating that it is 8.2 divided by 100 billion (10¹¹). This notation is useful when working with very small decimal fractions, such as in scientific measurements.

Powers of 10 notation with superscripts provides a clear and concise way to represent numbers across a wide range of scales, from the macroscopic to the microscopic, making it a fundamental concept in scientific notation.

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Answer:

c

Explanation: