# Could you please check my work and help me with a couple.

An airplane that flies at 100 km/h with a 10 km/h tailwind travels at 110 km/h relative to the ground. If it instead flies into a 10 km/h headwind, its groundspeed is :

110 km/h /2= 55 km/h

The average speed of a horse that gallops a distance of 10 kilometers in a time of 30 minutes is

(10 km)(30 min)= 300 km

What is the acceleration of a car that maintains a constant velocity of 100 km/hr for 10 seconds?

100 km/hr /10 s= 10 km/h s

Ten seconds after starting from rest, an object falling freely downward will have a speed of about (This question I don't understand)

It takes 6 seconds for a stone to fall to the bottom of a mine shaft. How deep is the shaft? (This one I don't understand)

If a projectile is fired straight up at a speed of 10 m/s, the total time to return to its starting position is about

would it be 10 m/s?

A man leans over the edge of a cliff and throws a rock upward at 4.9 m/s. How far below the level from which it was thrown is the rock 2 seconds later?

(4.9 m/s)(2 s)=9.8 m

1. An airplane that flies at 100 km/h with a 10 km/h tailwind travels at 110 km/h relative to the ground. If it instead flies into a 10 km/h headwind, its groundspeed is:

To find the groundspeed when flying into a headwind, we subtract the headwind speed from the airspeed:
100 km/h - 10 km/h = 90 km/h

So, the groundspeed when flying into a 10 km/h headwind is 90 km/h.

2. The average speed of a horse that gallops a distance of 10 kilometers in a time of 30 minutes is:

Average speed is calculated by dividing the total distance covered by the time taken:
Average speed = Distance / Time

Here, the horse galloped a distance of 10 kilometers in 30 minutes:
Average speed = 10 km / 30 min = 1/3 km/min

So, the average speed of the horse is 1/3 km/min.

3. What is the acceleration of a car that maintains a constant velocity of 100 km/hr for 10 seconds?

Acceleration measures the rate at which the velocity of an object changes. In this case, since the car maintains a constant velocity, the acceleration is zero. Therefore, the acceleration of the car is 0 km/hr^2.

4. Ten seconds after starting from rest, an object falling freely downward will have a speed of about:

When an object falls freely under gravity, its velocity increases at a constant rate of 9.8 m/s^2 (acceleration due to gravity). After 10 seconds, the object will have fallen for a distance of:
Distance = 1/2 * acceleration * time^2
Distance = 1/2 * 9.8 m/s^2 * (10 s)^2
Distance ≈ 490 m

So, after 10 seconds, the object will have a speed of about 490 m/s.

5. It takes 6 seconds for a stone to fall to the bottom of a mine shaft. How deep is the shaft?

To find the depth of the shaft, we can use the equation of motion for free fall:
Distance = 1/2 * acceleration * time^2
Distance = 1/2 * 9.8 m/s^2 * (6 s)^2
Distance = 176.4 m

Therefore, the depth of the shaft is 176.4 meters.

6. If a projectile is fired straight up at a speed of 10 m/s, the total time to return to its starting position is about:

When a projectile is fired straight up, it goes against gravity until it reaches its maximum height and then falls back to the ground. The time taken for the projectile to return to its starting position is twice the time taken to reach the maximum height.

The time taken to reach the maximum height can be calculated using the formula:
Time = (Initial velocity) / (acceleration due to gravity)
Time = 10 m/s / 9.8 m/s^2 ≈ 1.02 s

Therefore, the total time to return to its starting position is approximately 2 x 1.02 s = 2.04 seconds.

7. A man leans over the edge of a cliff and throws a rock upward at 4.9 m/s. How far below the level from which it was thrown is the rock 2 seconds later?

To find the distance below the starting level after 2 seconds, we can use the formula:
Distance = (Initial velocity) * (Time) + (1/2) * (Acceleration) * (Time)^2

Here, the initial velocity is 4.9 m/s and the time is 2 seconds. Since the rock is thrown upward, the acceleration (due to gravity) is negative (-9.8 m/s^2).

Distance = (4.9 m/s) * (2 s) + (1/2) * (-9.8 m/s^2) * (2 s)^2
Distance = 9.8 m + (-19.6 m) = -9.8 m

Therefore, the rock is 9.8 meters below the level from which it was thrown after 2 seconds.

## I can definitely help you with these questions! Let's go through each one and determine the correct answers.

1. The first question asks about the groundspeed of an airplane flying into a 10 km/h headwind. Since the airplane's speed is 100 km/h and the headwind is 10 km/h, we need to subtract the headwind speed from the airplane's speed. Therefore, the groundspeed would be 100 km/h - 10 km/h = 90 km/h.

2. The second question asks for the average speed of a horse that gallops a distance of 10 kilometers in a time of 30 minutes. To find average speed, we divide the distance traveled by the time taken. So, the average speed would be 10 km / (30 min/60 min per hour) = 20 km/h.

3. The third question is about the acceleration of a car that maintains a constant velocity of 100 km/h for 10 seconds. Acceleration is the rate of change of velocity, so if the car maintains a constant velocity, the acceleration is zero. Therefore, the acceleration would be 0 km/h/s.

4. The fourth question is about the speed of an object falling freely downward after 10 seconds. When an object falls freely under gravity, it experiences constant acceleration of approximately 9.8 m/s². After 10 seconds, the object will reach a speed of approximately 9.8 m/s. The unit is in meters per second (m/s).

5. The fifth question asks about the depth of a mine shaft if it takes 6 seconds for a stone to fall to the bottom. The depth of the shaft can be found using the formula for distance traveled during free fall: distance = (1/2) x acceleration x time². Since the acceleration due to gravity is approximately 9.8 m/s², and the time is 6 seconds, the depth of the shaft would be (1/2) x 9.8 m/s² x (6 s)² = 176.4 meters.

6. The sixth question is about the total time for a projectile fired straight up at a speed of 10 m/s to return to its starting position. The total time is the time taken to go up plus the time taken to come back down. Considering that the speed decreases due to gravity, the time to go up is 10 m/s divided by the acceleration due to gravity (approximately 9.8 m/s²). Therefore, the total time would be 2 x (10 m/s / 9.8 m/s²) = 2.04 seconds.

7. The seventh question asks for the distance below the level from which a rock is thrown after 2 seconds if it was thrown upward at a speed of 4.9 m/s. Since the rock is moving against the force of gravity, its speed will decrease over time. The distance traveled can be found using the formula for distance covered during free fall: distance = initial velocity x time + (1/2) x acceleration x time². Here, the initial velocity is 4.9 m/s, the time is 2 seconds, and the acceleration due to gravity is approximately 9.8 m/s². Plugging these values into the formula, the distance below the level from which the rock was thrown would be (4.9 m/s x 2 s) + (1/2) x 9.8 m/s² x (2 s)² = 9.8 meters.

I hope these explanations help you understand the questions and their solutions! Let me know if you have any further questions.