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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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