Question

Please guys need a help ASAP

Answer 1

***Be careful while writing the units in your exam. I have written answers in m/km as well as in m/m***

The correct answers are:

(2)
`30(m)/(km)` (or 0.03 m/m)

(3)
`960(m)/(km)` (and NO! The car will not make it because gradient of the hill is greater than the maximum gradient the car can climb) (or 0.960 m/m)

(4)
`53.33(m)/(km)` (and YES! The car WILL make it because gradient of the hill is less than the maximum gradient the car can climb) (or 0.053 m/m)

(5) Road-A's gradient:
`100(m)/(km)`, and Road-B's gradient:
`10(m)/(km)` (Road-B will be easier to ride up). (Road-A 0.1 m/m; Road-B 0.010 m/m)

(7)
`1325(ft)/(mi)` (and YES! Johnny's tricycle WILL fall apart)

(8)
`2272.72(m)/(km)` (or 2.27272 m/m)

(9)
`753.49(m)/(km)` (or 0.7535 m/m)— If the sign is important then it should be
`-753.49(m)/(km)` as the plane is descending (slope is negative).

(10)
`543.47(m)/(km)` (or 0.5435 m/m) — If the sign is important then it should be
`-543.47(m)/(km)` as the plane is descending (slope is negative).

Explanations:

Important notes:

1. Please see the picture attached with the answer for (few) question.
2. I shall use meter per kilometer (or feet/miles) unit for gradient for all the questions in explanation, as many parts in the question-sheet deal with this unit for gradient.

For all these questions, remember the following formula:

`Gradient = (vertical\thinspace distance)/(horizontal\thinspace distance) \\OR\\Gradient = (Rise)/(Run)`

(2) As you can see in the picture attached, the horizontal distance is 100km, and the vertical distance is 3000 m. Therefore, the gradient will be:

`Gradient = (3,000)/(100) = 0.03=30(m)/(km)`

(3) As you can see in the picture attached, the horizontal distance is 0.5km, and the vertical distance is 500-20=480m. Therefore, the gradient will be:

`Gradient = (480)/(0.5) = 960(m)/(km)`

As 960 > 500, the car will not make it.

(4) As you can see in the picture attached, the horizontal distance is 1.5km, and the vertical distance is 100-20=80m. Therefore, the gradient will be:

`Gradient = (80)/(1.5) = 53.33(m)/(km)`

As 53.33 < 500, the car WILL make it.

(5) The elevation is 500 m.

For Road-A (which is 5 km long):

`Gradient = (500)/(5) = 100(m)/(km)`

For Road-B (which is 50 km long):

`Gradient = (500)/(50) = 10(m)/(km)`

Since 10 < 100, therefore, we can say that Road-B will be easier to ride up.

(7) As you can see in the picture attached, the horizontal distance is 0.2mi, and the vertical distance is 300-35=265ft. Therefore, the gradient will be:

`Gradient = (265)/(0.2) = 1325(ft)/(mi)`

As 1325 > 100, Johnny's tricycle WILL fall apart.

(8) As you can see in the picture attached, the horizontal distance is 22km, and the vertical distance is 50000 m. Therefore, the gradient will be:

`Gradient = (50,000)/(22) = 2272.72(m)/(km)`

(9) As you can see in the picture attached, the horizontal distance is 4.3km, and the vertical distance is 3560-320=3240m. Therefore, the gradient will be:

`Gradient = (3240)/(4.3) = 753.49(m)/(km)`

(10) As you can see in the picture attached, the horizontal distance is 7.2km, and the vertical distance is 4567-654=3913m. Therefore, the gradient will be:

`Gradient = (3913)/(7.2) = 543.47(m)/(km)`

NOTE FOR QUESTIONS 9 and 10: One thing to note here is that, as the plane is descending, the gradient should be negative (as the path has a negative slope).