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Chapter 2: Problem 9

You drop a rock from a cliff. If air resistance is neglected, which of the following statements is (are) true? 1\. The speed of the rock will increase. 2\. The speed of the rock will decrease. 3\. The acceleration of the rock will increase. 4\. The acceleration of the rock will decrease. a) 1 b) 1 and 4 c) 2 d) 2 and 3

Short Answer

Expert verified
a) The speed of the rock will increase. b) The speed of the rock will decrease. c) The acceleration of the rock will increase. d) The acceleration of the rock will decrease. Answer: a) The speed of the rock will increase.

Step by step solution

01

Understand the motion of the rock in free fall

When a rock is dropped from a cliff, it is in free fall. In the absence of air resistance, the only force acting on the rock is gravity, which pulls the rock downward. The acceleration due to gravity (g) is constant (approximately 9.81 m/s^2).
02

Analyze statement 1

Statement 1 says that the speed of the rock will increase. As the rock is in free fall, it will accelerate downwards due to gravity. This means that its speed will increase in the downward direction. So, statement 1 is true.
03

Analyze statement 2

Statement 2 says that the speed of the rock will decrease. We have already determined in step 2 that the speed of the rock will increase, so statement 2 is false.
04

Analyze statement 3

Statement 3 says that the acceleration of the rock will increase. However, we know that the acceleration of the rock in free fall is constant (approximately 9.81 m/s^2) due to gravity. So, the acceleration does not increase. Hence, statement 3 is false.
05

Analyze statement 4

Statement 4 says that the acceleration of the rock will decrease. As we established in step 4, the acceleration of an object in free fall is constant (approximately 9.81 m/s^2). So, the acceleration does not decrease either. Statement 4 is false.
06

Conclude the correct answer

Looking at the given options, the correct answer is: a) 1 - Only statement 1 is true as it states that the speed of the rock will increase due to the constant acceleration caused by gravity.

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Most popular questions from this chapter

The 2007 world record for the men's 100 -m dash was \(9.77 \mathrm{~s}\). The third-place runner crossed the finish line in \(10.07 \mathrm{~s}\). When the winner crossed the finish line, how far was the third-place runner behind him? a) Compute an answer that assumes that each runner ran at his average speed for the entire race. b) Compute another answer that uses the result of Example 2.3, that a world- class sprinter runs at a speed of \(12 \mathrm{~m} / \mathrm{s}\) after an initial acceleration phase. If both runners in this race reach this speed, how far behind is the third-place runner when the winner finishes?

You drop a rock over the edge of a cliff from a height \(h\). Your friend throws a rock over the edge from the same height with a speed \(v_{0}\) vertically downward, at some time \(t\) after you drop your rock. Both rocks hit the ground at the same time. How long after you dropped your rock did your friend throw hers? Express your answer in terms of \(v_{0}, g,\) and \(h\).

A bullet is fired through a board \(10.0 \mathrm{~cm}\) thick, with a line of motion perpendicular to the face of the board. If the bullet enters with a speed of \(400 . \mathrm{m} / \mathrm{s}\) and emerges with a speed of \(200 . \mathrm{m} / \mathrm{s}\), what is its acceleration as it passes through the board?

A car travels at 22.0 mph for 15.0 min and 35.0 mph for \(30.0 \mathrm{~min}\). How far does it travel overall? a) \(23.0 \mathrm{~m}\) b) \(3.70 \cdot 10^{4} \mathrm{~m}\) c) \(1.38 \cdot 10^{3} \mathrm{~m}\) d) \(3.30 \cdot 10^{2} \mathrm{~m}\)

The position of an object as a function of time is given as \(x=A t^{3}+B t^{2}+C t+D .\) The constants are \(A=2.1 \mathrm{~m} / \mathrm{s}^{3}\) \(B=1.0 \mathrm{~m} / \mathrm{s}^{2}, C=-4.1 \mathrm{~m} / \mathrm{s},\) and \(D=3 \mathrm{~m}\) a) What is the velocity of the object at \(t=10.0 \mathrm{~s}\) ? b) At what time(s) is the object at rest? c) What is the acceleration of the object at \(t=0.50 \mathrm{~s} ?\) d) Plot the acceleration as a function of time for the time interval from \(t=-10.0 \mathrm{~s}\) to \(t=10.0 \mathrm{~s}\).
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