TRAMPOLINE You are jumping on a trampoline. Your height (in feet) above
the trampoline after seconds can be represented by . How
many seconds are you in the air?

Ask by Vaughn Young. in the United States

Jan 23,2025

Question

TRAMPOLINE You are jumping on a trampoline. Your height $$ y $$ (in feet) above the trampoline after $$ t $$ seconds can be represented by $$ y=-16 t^{2}+24 t $$. How many seconds are you in the air?

UpStudy AI · Accepted Answer

To determine how long you are in the air while jumping on the trampoline, we can analyze the given height function:

$$
y(t) = -16t^2 + 24t
$$

Here, $$ y(t) $$ represents your height above the trampoline at any time $$ t $$ seconds. You are "in the air" when your height $$ y(t) $$ is greater than 0.

**Steps to Find the Time in the Air:**

1. **Set $$ y(t) $$ to Zero:**
   
   To find when you land back on the trampoline, set $$ y(t) = 0 $$:

$$
   -16t^2 + 24t = 0
   $$

2. **Factor the Equation:**

$$
   t(-16t + 24) = 0
   $$

This gives two solutions:

$$
   t = 0 \quad \text{or} \quad t = \frac{24}{16} = 1.5 \text{ seconds}
   $$

3. **Interpret the Solutions:**

- $$ t = 0 $$ seconds is the moment you start jumping.
   - $$ t = 1.5 $$ seconds is when you land back on the trampoline.

**Conclusion:**

You are in the air from $$ t = 0 $$ seconds until $$ t = 1.5 $$ seconds. Therefore, the total time you are in the air is **1.5 seconds**.

**Answer:**  
You are in the air for 1.5 seconds.
You are in the air for 1.5 seconds.

TRAMPOLINE You are jumping on a trampoline. Your height (in feet) above
the trampoline after seconds can be represented by . How
many seconds are you in the air?

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TRAMPOLINE You are jumping on a trampoline. Your height (in feet) above the trampoline after seconds can be represented by . How many seconds are you in the air?