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) $30\frac{m}{km}$ (or 0.03 m/m)

(3) $960\frac{m}{km}$ (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) $53.33\frac{m}{km}$ (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: $100\frac{m}{km}$, and Road-B's gradient: $10\frac{m}{km}$ (Road-B will be easier to ride up). (Road-A 0.1 m/m; Road-B 0.010 m/m)

(7) $1325\frac{ft}{mi}$ (and YES! Johnny's tricycle WILL fall apart)

(8) $2272.72\frac{m}{km}$ (or 2.27272 m/m)

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

(10) $543.47\frac{m}{km}$ (or 0.5435 m/m) — If the sign is important then it should be $-543.47\frac{m}{km}$ 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:

$Gradient = \frac{vertical\thinspace distance}{horizontal\thinspace distance} \\OR\\Gradient = \frac{Rise}{Run}$

(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:

$Gradient = \frac{3,000}{100} = 0.03=30\frac{m}{km}$

(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:

$Gradient = \frac{480}{0.5} = 960\frac{m}{km}$

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:

$Gradient = \frac{80}{1.5} = 53.33\frac{m}{km}$

As 53.33 < 500, the car WILL make it.

(5) The elevation is 500 m.

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

$Gradient = \frac{500}{5} = 100\frac{m}{km}$

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

$Gradient = \frac{500}{50} = 10\frac{m}{km}$

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:

$Gradient = \frac{265}{0.2} = 1325\frac{ft}{mi}$

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:

$Gradient = \frac{50,000}{22} = 2272.72\frac{m}{km}$

(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:

$Gradient = \frac{3240}{4.3} = 753.49\frac{m}{km}$

(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:

$Gradient = \frac{3913}{7.2} = 543.47\frac{m}{km}$

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).