In basketball, hang time is the time that both of your feet are off the ground during a jump. The equation for hang time is [tex]$t=2\left(\frac{2 h}{32}\right)^{\frac{1}{2}}$[/tex], where [tex]$t$[/tex] is the time in seconds, and [tex]$h$[/tex] is the height of the jump, in feet.
Player 1 had a hang time of 0.9 s. Player 2 had a hang time of 0.8 s. To the nearest inch, how much higher did Player 1 jump than Player 2?
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Answer (2)
Player 1 jumped approximately 8 inches higher than Player 2. Player 1's jump height is calculated to be 3.24 feet, while Player 2's jump height is 2.56 feet, resulting in a height difference of 0.68 feet or approximately 8 inches. Thus, the final answer is 8 inches.
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Calculate Player 1's jump height h 1 using the given hang time t 1 = 0.9 s: 0.9 = 2 ( 32 2 h 1 ) 2 1 , which gives h 1 = 3.24 feet.
Calculate Player 2's jump height h 2 using the given hang time t 2 = 0.8 s: 0.8 = 2 ( 32 2 h 2 ) 2 1 , which gives h 2 = 2.56 feet.
Find the difference in jump heights: Δ h = h 1 − h 2 = 3.24 − 2.56 = 0.68 feet.
Convert the difference to inches and round to the nearest inch: 0.68 feet × 12 foot inches = 8.16 inches ≈ 8 inches. The final answer is 8 .
Explanation
Problem Analysis Let's analyze the problem. We are given the equation for hang time in terms of jump height, and we are given the hang times for two players. We need to find the difference in their jump heights to the nearest inch.
Calculating Player 1's Jump Height First, we need to find the jump height for Player 1. We are given that t 1 = 0.9 seconds. Plugging this into the equation, we have: 0.9 = 2 ( 32 2 h 1 ) 2 1 Dividing both sides by 2, we get: 0.45 = ( 32 2 h 1 ) 2 1 Squaring both sides, we get: 0.2025 = 32 2 h 1 Multiplying both sides by 32, we get: 6.48 = 2 h 1 Dividing both sides by 2, we get: h 1 = 3.24 feet So, Player 1's jump height is 3.24 feet.
Calculating Player 2's Jump Height Next, we need to find the jump height for Player 2. We are given that t 2 = 0.8 seconds. Plugging this into the equation, we have: 0.8 = 2 ( 32 2 h 2 ) 2 1 Dividing both sides by 2, we get: 0.4 = ( 32 2 h 2 ) 2 1 Squaring both sides, we get: 0.16 = 32 2 h 2 Multiplying both sides by 32, we get: 5.12 = 2 h 2 Dividing both sides by 2, we get: h 2 = 2.56 feet So, Player 2's jump height is 2.56 feet.
Finding the Difference in Jump Heights Now, we need to find the difference in jump heights: Δ h = h 1 − h 2 = 3.24 − 2.56 = 0.68 feet So, the difference in jump heights is 0.68 feet.
Converting to Inches and Rounding Finally, we need to convert the difference from feet to inches. Since there are 12 inches in a foot, we multiply by 12: 0.68 feet × 12 foot inches = 8.16 inches Rounding to the nearest inch, we get 8 inches.
Final Answer Therefore, Player 1 jumped 8 inches higher than Player 2.
Examples
Understanding hang time and jump height can be useful in sports training. Coaches can use these calculations to assess athletes' performance and tailor training programs to improve their jumping ability. For example, if a basketball player wants to increase their hang time, they can work on increasing their jump height through strength and plyometric exercises. By tracking their progress and using the hang time equation, they can see how their training is affecting their performance. This can also be applied in other sports like volleyball or track and field.
