Answer:
Actual speed of red car is 92.78 feet/s
Step-by-step explanation:
Consider A be the position of police car, B is the point of road from which the distance of police car measure and C is the point from which the red car is moving towards the point B as shown in the figure.
According to the figure,
AB = x, BC = z and AC = y.
According to the problem,
Distance between road and police car, x = 70 feet
Distance between police car and red car, y = 160 feet
Using Pythagoras theorem in the following figure,
(AC)² = (AB)² + (BC)²
y² = x² + z² ....(1)
Substitute the suitable values in the above equation.
y² = (160)² + (70)²
y = √30500
y = 174.64 feet
Differentiating equation (1) with respect to time t:
...(2)
According to the problem,
Position of police car is fixed with respect to road, so
is zero and
Distance between police car and red car is decreasing,

Hence equation (2) becomes:

Substitute the suitable values in the above equation.

