Hi I need help with these questions thank you.
A teacher walks around the room while students are taking a test. If he walks 8 m North, 6 m East, 8 m South, and 6 m West, what is his displacement?
28 m
0 m
22 m
A dog runs across the room at a constant speed. What is its acceleration?
0 m/s^2
-1 m/s^2
Not enough information
A car accelerates from rest to a speed of 18 m/s over a distance of 400 m. What is its acceleration?
3600 m/s^2
0.0225 m/s^2
0.405 m/s^2
A helicopter drops a bucket of water onto a forest fire from 38 meters above the blaze. How long does it take the water to fall and reach the flames?
744.8 s
2.74 s
7.76 s
A golf ball is hit horizontally from a 45 m tall building with a speed of 62.5 m/s. How far from the building does it land? (Hint: Find time first.)
573.8 m
20.6 m
189.4 m
How long will a soccer ball that is kicked at 6 m/s at an angle of 27 degrees above the horizontal take to hit the ground downfield?
0.75 s
0.56 s
1.1 s
pls help
Sure! I'll be happy to help you with these questions. Let's go through each one step by step.
Question 1:
To find the teacher's displacement, we need to determine the straight-line distance and direction from the starting point to the final position after all the walking. We can use the Pythagorean theorem to solve this.
The teacher walks 8 m North and then 8 m South, which cancel each other out. Similarly, he walks 6 m East and then 6 m West, which also cancel each other out. Therefore, his net displacement is 0 m.
Answer: 0 m
Question 2:
Acceleration is a measure of how an object's velocity changes over time. Since the dog is running at a constant speed, its velocity is not changing, which means there is no acceleration.
Answer: 0 m/s^2
Question 3:
Acceleration is the rate at which an object's velocity changes. In this case, the car starts from rest (0 m/s) and reaches a final speed of 18 m/s over a distance of 400 m. To find acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time
Since the car starts from rest, the initial velocity is 0 m/s. We are given the final velocity (18 m/s) and the distance (400 m), but we need to find the time. We can use another formula:
final velocity^2 = initial velocity^2 + 2 * acceleration * distance
Plugging in the numbers, we can solve for time, and then substitute it back into the first formula to find acceleration.
Answer: 0.405 m/s^2
Question 4:
To find how long it takes the water to fall and reach the flames, we can use the equation:
distance = 0.5 * acceleration * time^2
In this case, the distance is 38 m and the acceleration is due to gravity, which is approximately 9.8 m/s^2. Plugging these values into the equation and solving for time will give us the answer.
Answer: 2.74 s
Question 5:
To find how far the golf ball lands from the building, we need to calculate the horizontal distance it travels. Since it is hit horizontally, there is no vertical acceleration involved.
We can use the equation:
distance = initial velocity * time
For the horizontal motion, the initial vertical velocity is 0 m/s, and the acceleration due to gravity is also 0 m/s^2. Using this information, we can find the time it takes for the ball to reach the ground. Then, we can plug this time into the equation to calculate the horizontal distance.
Answer: 189.4 m
Question 6:
To find how long it takes for the soccer ball to hit the ground, we can analyze the vertical motion. The initial vertical velocity is given as 6 m/s, and the angle of 27 degrees above the horizontal tells us that the initial horizontal velocity is 6 * cos(27).
Using the equation:
vertical distance = (initial vertical velocity * time) + (0.5 * acceleration * time^2)
The vertical distance is 0, as the ball hits the ground. The acceleration due to gravity is approximately -9.8 m/s^2. Plugging in the known values and solving for time will give us the answer.
Answer: 0.75 s
I hope this helps! Let me know if you have any further questions.