We appreciate your visit to 5 A toy rocket is launched from the ground with an acceleration tex a tex a If the rocket runs out of fuel after 2. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
The toy rocket reaches a maximum height of 44.1 m, begins its descent around 3.04 seconds, stays in the air for about 5.14 seconds, and has a velocity of -9.43 m/s just before hitting the ground.
Explanation:
Solution to the Toy Rocket Launch Problem
A toy rocket launched from the ground experiences different motions during its flight. Let's break down each part of the problem:
- a. Maximum Height Calculation:
The rocket accelerates upwards to a final velocity of 20 m/s in 1 second. Using the kinematic equation for displacement, we get:
Displacement (s) = initial velocity (u) time (t) + 0.5 acceleration (a) t2
Here, since the initial velocity u = 0 m/s, and acceleration (a) can be calculated as:
a = (final velocity - initial velocity) / time = (20 m/s - 0 m/s) / 1 s = 20 m/s2
So, the maximum height achieved after fuel runs out (2.1 seconds) is:
Height = (0 m/s 1s) + 0.5 (20 m/s2) (2.1 s)2 = 0 + 0.5 20 4.41 = 44.1 m.
- b. Descent Start Time:
The rocket runs out of fuel at 2.1 seconds. The time when the rocket reaches its maximum height can be found using the equation:
Time to peak = (initial velocity) / (gravity) = (20 m/s) / (9.81 m/s2) ≈ 2.04 seconds.
Thus, the rocket begins to descend shortly after 2.1 seconds, around 3.04 seconds.
- c. Total Time in the Air:
If the rocket is in free fall for approximately 1.04 seconds after it runs out of fuel, then the total time until it hits the ground can be calculated:
Total time = time ascending + descent // (to reach max height) + (falling time + time with parachute). Assuming it takes 1 second for the parachute to deploy and the rest is constant velocity fall.
Total time = 2.1 s (ascent) + 1.04 s (free fall) + 2 s = 5.14 seconds.
- d. Velocity Before Hitting Ground:
Finally, we can find the velocity just before it hits the ground. Assuming it falls for approximately 3 seconds (from 2.1 s to around 5.14 s), using v = u + at = 20 m/s - (9.81 m/s2 * 3 s) gives:
Velocity just before hitting ground = 20 m/s - 29.43 m/s = -9.43 m/s (downward).
In conclusion, the rocket reaches a maximum height of about 44.1 m, begins descending around 3.04 s, and the total time in the air is approximately 5.14 s with a velocity of -9.43 m/s just before impact.
Learn more about rocket motion here:
https://brainly.com/question/49965881
Thanks for taking the time to read 5 A toy rocket is launched from the ground with an acceleration tex a tex a If the rocket runs out of fuel after 2. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
