A rocket is fired upward from ground level with an initial velocity of 480km/hr. after t seconds its distance above the ground level is given by 480t_16t²
for what time interval is the rocket more than 3200km above ground level
You have mixed up all your units. 480 km/hr does not translate to 480t unless t is in hours. Also, that -16t^2 looks like English units with g = -32 ft/s^2
But let's just go with your numbers as given, and assume that the height is given in km, after t hours, and g = -32 km/hr^2. Then just solve
480t - 16t^2 > 3200
t^2 - 30t + 200 < 0
(t-10)(t-20) < 0
10 < t < 20
so 10 hours.
Thank you very mach
I owe you one bro thanks
Well, let's use a little bit of math and humor to figure this out, shall we?
First, let's set up an equation to find the time interval when the rocket is more than 3200 km above the ground level. We have the equation for the distance above the ground level: 480t - 16t².
To find the time interval when the rocket is more than 3200 km above ground level, we need to solve the inequality 480t - 16t² > 3200.
Now, we could solve this inequality using complicated math and formulas, but since I'm a clown bot, I like to simplify things. So, let's make this fun!
Imagine the rocket as a clown rocket, flying high up in the sky. The distance above the ground level represents how high the clown rocket is flying.
Now, let's imagine there's a hurdle at 3200 km. The clown rocket needs to jump over this hurdle to be higher than 3200 km above the ground level.
So, the equation becomes: 480t - 16t² > 3200. We want to find the time interval when the clown rocket jumps over the 3200 km hurdle.
To solve this, let's set up a little joke:
Why did the clown rocket go on a diet?
Because it wanted to jump higher and clear that 3200 km hurdle!
So, the clown rocket needs to lose some weight, represented by the term -16t² in the equation. By losing weight, it can jump higher and go above the 3200 km hurdle.
Now, let's find the time interval when the clown rocket is higher than 3200 km above the ground level.
Setting up our equation, 480t - 16t² > 3200, we can rearrange it to:
16t² - 480t + 3200 < 0.
Now we can solve this equation to find the time interval when the clown rocket is above 3200 km.
To find the time interval in which the rocket is more than 3200 km above ground level, we need to set up an inequality using the given equation for the distance above ground level.
The equation for the distance above ground level is given as 480t - 16t², where t represents time in seconds. To find the time interval when the rocket is more than 3200 km above ground level, we set up the inequality:
480t - 16t² > 3200
To solve this inequality, we need to rearrange the terms and bring everything to one side:
16t² - 480t + 3200 < 0
Now, we have a quadratic inequality. To solve it, we can factorize or use the quadratic formula.
Factorizing the quadratic, we get:
16(t - 40)(t - 20) < 0
Now, we need to find the critical points that divide the number line into different intervals. The critical points are the values of t that make the expression equal to zero:
(t - 40) = 0 or (t - 20) = 0
Solving these equations:
t - 40 = 0 --> t = 40
t - 20 = 0 --> t = 20
Now, we have three intervals on the number line: (-∞, 20), (20, 40), and (40, +∞).
We select a test value from each interval and check the signs of the expression:
For t < 20: If we substitute t = 10 into the inequality: 16(10 - 40)(10 - 20) < 0, we get a negative value.
For 20 < t < 40: If we substitute t = 30 into the inequality: 16(30 - 40)(30 - 20) < 0, we get a positive value.
For t > 40: If we substitute t = 50 into the inequality: 16(50 - 40)(50 - 20) < 0, we get a negative value.
Based on the signs, we can now conclude that the rocket is more than 3200 km above ground level for the time interval (20, 40) seconds.