a straight road is inclined 30 degees to the horizontal and a man is walking along the road at the rate of 2 and a half miles an hour. how many feet does he ascend vertically against the force of gravity in 15 minutes?
sin30 = 0.5
That means that for every mile traveled on the road (hypotenuse), he rises .5 miles in elevation (opposite side).
So, since 15 min = .25 hr, he has traveled 2.5 * .25 = .625 miles, and gained .3125 miles = 1650 ft in elevation.
That's some steep grade: 50%!
thanks steve! :)
To find the vertical ascent in 15 minutes, we need to calculate two components: the horizontal distance covered and the vertical distance covered.
First, let's calculate the horizontal distance covered by the man in 15 minutes. We know that the man is walking at a speed of 2.5 miles per hour, which means he covers a distance of 2.5 miles in one hour. To convert this to minutes, we divide by 60 (since there are 60 minutes in an hour):
Horizontal distance covered = (2.5 miles / 60 minutes) * 15 minutes
Next, let's calculate the vertical distance covered by the man as he ascends along the inclined road. The vertical distance covered is equal to the horizontal distance multiplied by the tangent of the angle of inclination.
Vertical distance covered = Horizontal distance covered * tan(angle of inclination)
In this case, the angle of inclination is given as 30 degrees.
Finally, we convert the resulting vertical distance from miles to feet, as per the request.
To summarize the calculation steps:
1. Calculate the horizontal distance covered: (2.5 miles / 60 minutes) * 15 minutes.
2. Calculate the vertical distance covered: Horizontal distance * tan(30 degrees).
3. Convert the vertical distance from miles to feet.
Now, let's calculate the answer using these steps:
Horizontal distance covered = (2.5 miles / 60 minutes) * 15 minutes = 0.625 miles
Vertical distance covered = 0.625 miles * tan(30 degrees)
To convert from miles to feet, we know that 1 mile is equal to 5280 feet. So, we can multiply the vertical distance covered (in miles) by 5280 to get the final answer in feet.
Vertical distance covered = (0.625 miles * tan(30 degrees)) * 5280 feet
Now you can calculate the final answer.