Question

On a highway with a steep incline, the runaway truck ramp is constructed so that a vehicle that has lost its brakes can stop. The ramp is designed to slow a truck in succeeding 20-m distances by 10km/h, 12km/hr, 14km/hr,.....If the ramp is 160 m long, will it stop a truck moving 120km/hr (75 miles/hr) when it reached the ramp?

Answer 1

We can find the maximum speed of a truck that can be brought to a halt over the entire course of 160 m of the ramp.

We are given the speed that it is able to reduce over every successive 20 m stretch, hence there will be 8 such value reductions. Thus, the maximum speed which the ramp can handle i.e. bring a truck with that speed to halt, is

We can find this sum using the formula for the sum of an Arithmetic Progression with numbers of terms, n = 8, first term a = 10 and common difference, d = 2

The ramp can stop a truck running at a maximum speed of 136 km/hr. So yes, it can very much stop the truck running at 120 km/hr (75 miles/hr) with some fair distance still remaining on the ramp