The speed limit on suburban roads is 50 km/h. You are traveling at the limit when an empty bag blows onto the road from behind a parked car 5.0m in front of you. If you maintain your speed how long will it be before you hit?

Niagara Falls is about 50.0 km from Buffalo. A freight train starts out from Buffalo for Niagara Falls at 50.0 km/h. At the same time, a passenger train leaves Toronto for Ajax at 75 km/h. How much time passes before they meet one another, in minutes?

What is the speed of a water bomb after 1.75 s if it is released from rest at a height of 110m above the ground and how high off the ground is the ball?

Can you show your work as well?

To calculate the time it will take before you hit the bag:

1. Convert the speed limit from km/h to m/s:
Speed limit = 50 km/h = 50,000 m/60 min = 833.33 m/min = 13.89 m/s

2. Convert the distance from meters to kilometers:
Distance = 5.0 m = 5.0 x 10^-3 km

3. Divide the distance by the speed to get the time:
Time = Distance / Speed
Time = 5.0 x 10^-3 km / 13.89 m/s

Calculating the time passes before the bag hits:
Time = 0.00036 s (rounded to four decimal places)

To calculate the time it takes for the two trains to meet:

1. Convert the distance from km to m:
Distance = 50.0 km = 50,000 m

2. Calculate the relative speed of the two trains:
Relative speed = Speed of train A + Speed of train B
Relative speed = 50.0 km/h + 75 km/h

3. Convert the relative speed from km/h to m/s:
Relative speed = (50.0 km/h + 75 km/h) x (1000 m/3600 s)

4. Divide the distance by the relative speed to get the time:
Time = Distance / Relative speed
Time = 50,000 m / [(50.0 km/h + 75 km/h) x (1000 m/3600 s)]

Calculating the time passes before the two trains meet:
Time = 1 hour 27 minutes 16 seconds

To calculate the speed of the water bomb after 1.75 seconds:

1. Use the formula for calculating the velocity of an object in free fall:
Velocity = sqrt(2gh)

where g is the acceleration due to gravity and h is the height from which the object is dropped.

2. Convert the height from meters to kilometers:
Height = 110 m = 110 x 10^-3 km

3. Calculate the velocity:
Velocity = sqrt(2gh)
Velocity = sqrt(2 x 9.8 m/s^2 x 110 x 10^-3 km)

Calculating the speed of the water bomb after 1.75 seconds:
Velocity = 42.03 m/s (rounded to two decimal places)

To calculate how high off the ground is the ball after 1.75 seconds:

1. Use the formula for calculating the height of an object in free fall:
Height = (1/2)gt^2

where g is the acceleration due to gravity and t is the time.

2. Calculate the height:
Height = (1/2)gt^2
Height = (1/2) x 9.8 m/s^2 x (1.75 s)^2

Calculating the height off the ground after 1.75 seconds:
Height = 15.17 m (rounded to two decimal places)

Summary of results:

- Time before you hit the bag: 0.00036 s
- Time before the two trains meet: 1 hour 27 minutes 16 seconds
- Speed of the water bomb after 1.75 seconds: 42.03 m/s
- Height off the ground after 1.75 seconds: 15.17 m

Sure! I can help you solve these problems and show you the steps to find the answers.

1. To find how long it will be before you hit the bag on the road, we can start by converting the speed limit to meters per second. Since 1 km = 1000 m and 1 hour = 3600 seconds, the speed limit of 50 km/h can be converted to meters per second by multiplying it by 1000/3600. So, the speed limit is approximately 13.89 m/s.

Next, we need to calculate the time it takes for you to cover the distance between you and the bag. The distance is given as 5.0 m. We can use the formula time = distance / speed to find the time. Plugging in the values, we have time = 5.0 m / 13.89 m/s. Calculating this will give us the answer.

2. To find how much time passes before the freight train and the passenger train meet, we can use the concept of relative speed. The relative speed is the sum of their speeds since they are moving towards each other. Starting with the given speeds of 50.0 km/h for the freight train and 75 km/h for the passenger train, we need to convert them to meters per second using the same methodology as explained in the previous problem.

After converting both speeds to meters per second, we can find the relative speed by adding them. Once we have the relative speed, we can use the formula time = distance / speed to find the time it takes for them to meet. The distance is given as 50.0 km (which can also be converted to meters) since that is the distance between Niagara Falls and Buffalo. Plugging in the values will give us the answer.

3. To find the speed of the water bomb after 1.75 seconds, we can use the equation of motion for an object in free fall. The equation is h = 0.5 * g * t^2, where h is the height, g is the acceleration due to gravity, and t is the time. The acceleration due to gravity is approximately 9.8 m/s^2.

Using the given height of 110 m and the time of 1.75 seconds, we can rearrange the equation to solve for the speed. The equation becomes v = sqrt(2 * g * h), where v is the velocity or speed of the water bomb.

Finally, to find how high off the ground the ball is, we can rearrange the equation h = 0.5 * g * t^2 and solve for h using the given time of 1.75 seconds.

By following these steps and plugging in the given values, you should be able to find the answers to these problems.

50 km/h = 50000 m/3600 second

= 129/5 m/s
= 25.8 m/s

129/5 = 5/s
129s = 25
s = 25/129 seconds or approx .2 seconds
brace yourself, you are going to hit it

Your second question makes no sense.
Whoever made it up is poor in geography.
Buffalo is in the US, Niagara Falls is in Canada. (There is a
Niagara Falls, NY, with about half the population of the Canadian city)
Toronto and Ajax are both on the north side of Lake Ontario in Canada, just google it. So how can they meet ???

third question
velocity in freefall = -9.8t^2 , t in seconds, velocity in m/s
velo. = 1.75(-9.8) or -17.15 m/s
The negative shows the direction of the fall

distance in freefall = 4.9t^2
so after 1.75 s it has fallen 4.9(1.75)^2 = 15 m
so distance above the ground = 110-15 = 85 m