Gradient

A ramp to allow wheelchair access to a school has the dimensions shown below.

The maximum gradient allowed for a ramp with a horizontal distance of 4 m is $\displaystyle \frac{1}{14}.$

Does the gradient of this ramp meet the regulations?
Use your working to justify your answer.

Sarah's driveway is sloped as shown in the diagram below.

The cross-section of the driveway is in the shape of a right-angled triangle.

The base is 4 metres long and makes an angle of 12° with the driveway as shown in the diagram below.

(a) Construct a scale drawing of the cross-section of the driveway. Use a scale of 1 cm : 0.5 m.

(b) Use your scale drawing to calculate the gradient of the driveway.

Tracy decides to walk to the top of Dumyat Hill from Blairlogie car park.

• The horizontal distance between these two places is 3 kilometres.
• Blairlogie car park is 21 metres above sea level.
• The top of Dumyat Hill is 420 metres above sea level.

Calculate the average gradient between the Blairlogie car park and the top of Dumyat Hill.
Give your answer as a fraction in its simplest form.

To improve his fitness Andy wants to complete hill sprints.
The hill closest to his house has the following measurements:
The horizontal distance between the top and the bottom of the hill is 250 metres.
The bottom of the hill is 48 metres above sea level.
The top of the hill is 71 metres above sea level.

His training programme states that the hill must have a gradient greater than 0.1.

(b) Determine if the gradient of this hill meets this requirement.