Question

Johnny is riding his favorite red tricycle and is getting ready to go down a hill. His mommy warned him that his tricycle will fall apart if he goes down a hill with a slope greater than 100ft/mi. Johnny ignores his mommy and takes on the hill, which goes from 300ft all the way down to 35ft. The distance he travels is 0.2 miles. Calculate the gradient of the hill and determine if Johnny's tricycle will fall apart.

Answer 1

The gradient of the hill Johnny is riding down is calculated to be 1325.28ft/mi, which exceeds the safe limit of 100ft/mi given by his mommy. Hence, it is determined that Johnny's tricycle will fall apart.

Step-by-step explanation:

The student is asking us to calculate the gradient of the hill that Johnny is riding his tricycle down and to determine if the tricycle will fall apart based on the gradient. The slope of a hill is calculated by finding the difference in height divided by the horizontal distance traveled.

To find the gradient of the hill, we use the formula:

Gradient = (Change in elevation) / (Distance traveled)

Johnny's hill changes in elevation from 300ft to 35ft, which is a change of 300ft - 35ft = 265ft. The distance traveled is 0.2 miles. Since we know 1 mile = 5280 feet, we can convert 0.2 miles to feet:

0.2 miles * 5280 feet/mile = 1056 feet

Now we can calculate the gradient:

Gradient = 265ft / 1056ft = 0.251ft/ft

To get the slope in ft/mi, necessary to determine if the tricycle will fall apart, we convert the gradient:

Gradient = 0.251ft/ft * 5280ft/mi = 1325.28ft/mi

Johnny's mommy warned him that the tricycle will fall apart if the hill's slope is greater than 100ft/mi. The slope of Johnny's hill is 1325.28ft/mi, which is greater than 100ft/mi. Therefore, based on this calculation, Johnny's tricycle will unfortunately fall apart.