Answer:
75.9 km/hr
Step-by-step explanation:
Distance between the highway and farmhouse is given as = 2km = a
The distance after the intersection and the highway = b
Let the distance between the farmhouse and the car = c
Using the Pythagoras Theorem rule
c² = a² + b²
c² = 2² + b²
Step 1
Since distance is involved, time is required. Hence, we differentiate the equation above in respect to time
c² = 2² + b²
dc/dt (2c) = 4 + 2b
dc/dt =[ b/(√b² + 4)] × db/dt
We are told in the question that:
the car travels past the farmhouse on on the highway at a speed of 80 km/h.
We are asked to calculate the speed at which the distance between the car and the farmhouse kept increasing when the car is 6 km past the intersection of the highway and the road.
This calculated using the obtained differentiation above:
dc/dt = [ b/(√b² + 4)] × db/dt
Where b = 6km
db/dt = 80km/hr
[6/(√6² + 4)] × 80km/hr
6/√36 + 4 × 80km/hr
6 × 80/√40
480/√40
= 75.894663844km/hr
Approximately = 75.9km/hr
