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Calculating Cliff Height Using Fall Time: Examples and Exercises

In this guide, we explore how to calculate the height of cliffs based on the time an object falls. Using the expression (16t^2), where (t) is the time in seconds, we demonstrate with examples: a stone falling for 5 seconds hits the water from a 400-foot cliff, while a stone that takes 8 seconds to hit calculates to a height of 1024 feet. We also discuss the proper order of operations for evaluating expressions, including powers, addition, and subtraction, to ensure accuracy in calculations.

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Calculating Cliff Height Using Fall Time: Examples and Exercises

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  1. 16 (5)2 = = 16 (25) ANSWER The height of the cliff is 400 feet. EXAMPLE 3 Using a Power Cliff Height A stone falls over the edge of a cliff next to a waterfall. The stone hits the water 5 seconds later. How tall is the cliff? To find the height of the cliff use the expression 16t 2, the distance in feet that an object falls in t seconds after it begins to fall. 16 t2 Substitute 5 for t. Evaluate the power. = 400 Multiply.

  2. (6 - 4)3 3 22 – = – 23 + 3 22 a. + – 8 3 4 + = EXAMPLE 4 Using the Order of Operations Evaluate the expression. Evaluate inside grouping symbols. Evaluate powers. Add and subtract from left to right. = 7

  3. b. 3.3 (7 1)2 42 + = 64 16 3.3 = 3.3 82 42 EXAMPLE 4 Using the Order of Operations Evaluate inside grouping symbols. Evaluate powers. Multiply and divide from left to right. = 13.2

  4. = – – 8. (5 2)3 7 43 + (3)3 – 7 + 43 for Examples 3 and 4 GUIDED PRACTICE Evaluate the expression. Evaluate inside grouping symbols. = 27 – 7 + 64 Evaluate powers. = 20 + 64 Subtract. = 84 Add.

  5. – – 12.3 + (6)2 24 = 9. 12.3 + (4 + 2)2 24 for Examples 3 and 4 GUIDED PRACTICE Evaluate the expression. Evaluate inside grouping symbols. = 12.3 + 36 – 16 Evaluate powers. = 12.3 +20 Add. = 32.3

  6. – 10. 73 + 24 (7 6)4 = 73 + 24 (1)4 for Examples 3 and 4 GUIDED PRACTICE Evaluate the expression. Evaluate inside grouping symbols. Evaluate powers. = 73 +24 = 343 + 24 Add. = 367

  7. 16 (8)2 = = 16 (64) ANSWER The height of the cliff is 1024 feet. for Examples 3 and 4 GUIDED PRACTICE 11. What If? Suppose the falling stone in Example 3 took 8 seconds to hit the water. Evaluate the expression to find the height of the cliff. 16 t2 Substitute 8 for t. Evaluate the power. = 1024 Multiply.

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