The length of the diagonal will be 538.5 ft. Then the rate at which the angle from the man to the car is changing at the same moment will be 46.43 ft/s.
What is speed?
The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
A man stands 200 ft to the left of where a car starts moving north. The car is moving at 50ft/sec.
The rate at which the diagonal distance from the man to the car is changing once the car has been traveling for 10 seconds. Then the length of the diagonal will be
L² = x² + y²
L² = 200² + (50 × 10)²
L² = 40000 + 250000
L² = 290000
L = 538.50 ft
Then the rate at which the angle from the man to the car is changing at the same moment will be
L² = x² + y²
Differentiate with respect to time, then we have
2L (dL/dt) = 0 + 2y (dy/dt)
2(538.5) (dL/dt) = 2 (500) (50)
dL/dt = 46.43 ft/sec
More about the speed link is given below.
https://brainly.com/question/7359669
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