An airplane is being floen at 1500km/h at 100m above level ground. The ground began to rise up at 10 degrees. How much time does the pilot have to madke correction such that the plane doesn't hit the ground?

the part where the ground is rised to 10 degrees confuses me.

You know the height is 100m. If the angle is 10 degrees, calculate tan angle = 100m/x where x will be the forward distance to reach the 100m height. Then use distance = rate x time to calculate time required. It will be VERY short. Don't forget to change km to m and remember the answer will be in hours.

10 seconds

To solve this problem, we need to use trigonometry and the formula for distance, rate, and time.

Let's break it down step by step:

1. First, we need to find out the distance along the ground that the plane needs to travel in order to reach the 100m height. We can use the tangent function to calculate this. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height (100m) and the adjacent side is the distance we need to find (x). So tan(10 degrees) = 100m / x.

2. Now, let's solve for x. We can rearrange the formula by multiplying both sides by x and then dividing both sides by tan(10 degrees). This gives us x = 100m / tan(10 degrees). Using a calculator to evaluate tan(10 degrees), we find that tan(10 degrees) is approximately 0.1763.

Therefore, x = 100m / 0.1763 ~= 567.14m.

3. Now that we know the distance the plane needs to cover along the ground, we can use the formula distance = rate x time to calculate the time required. The rate is given as 1500 km/h, which needs to be converted to meters per hour. To convert km to m, we need to multiply the rate by 1000, so the rate becomes 1500 km/h * 1000 = 1500000 m/h.

Plugging in the values into the formula: 567.14m = 1500000 m/h * time.

4. Solve the equation for time: time = 567.14m / 1500000 m/h. The units cancel out, leaving us with time in hours.

Calculating this on a calculator, we find that time is approximately 0.0003781 hours.

5. Finally, we need to convert hours to seconds since the question asks for the time in seconds. There are 3600 seconds in an hour, so we multiply the time in hours by 3600.

0.0003781 hours * 3600 seconds/hour ~= 1.36 seconds.

Therefore, the pilot has approximately 1.36 seconds to make the correction before the plane hits the ground.