Suppose we launch a scientific rocket straight up from sea level (at standard conditions) with a pressure measuring device attached to it. Given that in the first 12 seconds the rocket experiences a 25% decrease in air pressure, what is the average speed (rate of climb) of the rocket in these first 12 seconds (in metres per second)?
To find the average speed (rate of climb) of the rocket in the first 12 seconds, we need to know the change in altitude or height of the rocket.
In this question, we are given that the rocket experiences a 25% decrease in air pressure in the first 12 seconds. However, this information alone is not sufficient to determine the rate of climb.
To find the average speed, we need to know the change in altitude or the initial and final altitudes of the rocket. The air pressure alone does not directly provide this information.
If we assume that the change in air pressure is directly proportional to the change in altitude, we can proceed with an estimation.
First, we need to understand that air pressure decreases as altitude increases. This is due to the decrease in atmospheric density with increasing altitude.
Let's assume that the initial air pressure at sea level is P0 and the pressure after 12 seconds is P1.
Given that the rocket experiences a 25% decrease in air pressure, we can express this mathematically:
P1 = P0 - 0.25 * P0
P1 = 0.75 * P0
Now, let's assume that the change in altitude is proportional to the change in air pressure. If h0 is the initial altitude and h1 is the final altitude, we can write:
h1 = h0 - 0.25 * h0
h1 = 0.75 * h0
To find the rate of climb (average speed), we need to determine the change in altitude per unit time. Since we are given the time interval of 12 seconds, we can divide the change in altitude by the time:
average speed = (h1 - h0) / 12
Substituting the value of h1, we get:
average speed = (0.75 * h0 - h0) / 12
average speed = -0.25 * h0 / 12
average speed = -h0 / (4 * 12)
Therefore, the average speed of the rocket in the first 12 seconds would depend on the initial altitude (h0). Without the initial altitude, we cannot determine the exact average speed.