Question

A rocket, launched from rest, steadily increases speed to 25m/s over a 2.80s interval before exhausting all the fuel. The rocket continues upward but slows steadily to a stop 1.8s after running out of fuel.

How far did the rocket rise while burning fuel?

Whats the maximum height it gets to?

please help i cant do this for the life of me

Answer 1

Answer & Step-by-step explanation:

To find the distance the rocket rose while burning fuel, we can use the average velocity formula:

Average velocity = (final velocity + initial velocity) / 2

In this case, the initial velocity is 0 m/s since the rocket was launched from rest. The final velocity is 25 m/s, and the time interval is 2.8 seconds. Plugging these values into the formula, we have:

Average velocity = (25 m/s + 0 m/s) / 2

Average velocity = 12.5 m/s

Now, we can use the equation for distance traveled:

Distance = Average velocity * time

Plugging in the average velocity of 12.5 m/s and the time interval of 2.8 seconds, we get:

Distance = 12.5 m/s * 2.8 s

Distance = 35 meters

Therefore, the rocket rose 35 meters while burning fuel.

To find the maximum height the rocket reaches, we need to calculate the distance traveled during the time interval after running out of fuel. The time interval is given as 1.8 seconds.

Since the rocket is slowing down, we can use the same formula:

Distance = Average velocity * time

The average velocity is 25 m/s, and the time interval is 1.8 seconds. Plugging these values into the formula, we have:

Distance = 25 m/s * 1.8 s

Distance = 45 meters

Therefore, the maximum height the rocket reaches is 45 meters.

Answer 2

Explanation:

AI-generated answer

The distance the rocket rises while burning fuel can be found by calculating the area under the velocity-time graph during the time interval when the rocket is accelerating.

To do this, we can divide the time interval into two parts: the time it takes to reach 25 m/s and the time it takes for the rocket to slow down after running out of fuel.

1. First, let's calculate the distance traveled while the rocket is accelerating. We can use the formula:

distance = average velocity * time

Since the rocket starts from rest, the average velocity is half of the final velocity. So, the distance traveled during acceleration is:

distance1 = (25 m/s / 2) * 2.80 s

2. Next, let's calculate the distance traveled while the rocket is slowing down. The rocket slows down for 1.8 seconds after running out of fuel, and we know it comes to a stop. Therefore, the distance traveled during deceleration is:

distance2 = 0.5 * 0 m/s * 1.8 s

3. Now, let's add the two distances together to find the total distance the rocket rises while burning fuel:

total distance = distance1 + distance2

4. Finally, calculate the total distance:

total distance = (25 m/s / 2) * 2.80 s + 0.5 * 0 m/s * 1.8 s

total distance = 35 m

So, the rocket rises 35 meters while burning fuel.

To find the maximum height the rocket reaches, we need to consider its motion after running out of fuel. Since the rocket is slowing down, it will reach its maximum height at the point where its velocity becomes zero.

The time it takes for the rocket to slow down after running out of fuel is 1.8 seconds. We can calculate the height using the formula:

height = initial velocity * time + (1/2) * acceleration * time^2

Since the rocket is slowing down, its acceleration is negative. We can use the equation for deceleration:

height = initial velocity * time + (1/2) * acceleration * time^2

height = 25 m/s * 1.8 s + (1/2) * (-9.8 m/s^2) * (1.8 s)^2

height = 22.5 m - 15.876 m

height ≈ 6.62 m

Therefore, the rocket reaches a maximum height of approximately 6.62 meters.