A child operating a radio-controlled model car on a dock accidentally steers it off the edge. The car's displacement 0.65 s after leaving the dock has a magnitude of 8.4 m. What is the car's speed at the instant it drives off the edge of the dock?
0.65 s after leaving dock, vertical velocity component is
Vy = gt = 6.37 m/s
Vertical displacement will be
y = (1/2)gt^2 = 2.07 m
Horizontal displacement must be
X = sqrt[8.4^2 - (2.07)^2] = 8.14 m
Horizontal velocity component must be
Vx = X/0.65s = 12.52 m/s
That is also the speed as it leaves the edge of dock
To find the car's speed at the instant it drives off the edge of the dock, we need to determine the magnitude of its velocity at that moment. Velocity is the rate of change of displacement with respect to time.
Since the car's displacement is given as 8.4 m at 0.65 s after leaving the dock, we can calculate its average velocity during that time interval by dividing the displacement by the time:
Average velocity = Displacement / Time = 8.4 m / 0.65 s
Now, average velocity gives us an idea of the car's motion during the entire time interval, but we want to find its speed at the instant it drives off the edge of the dock. To do that, we need to consider that the car's velocity is likely changing continuously.
To estimate the car's speed at the instant it drives off the edge of the dock, we can assume that the car's velocity is approximately constant during the short time interval of 0.65 seconds. Therefore, we can say that the average velocity calculated earlier is approximately equal to the car's speed at that instant.
Hence, the car's speed at the instant it drives off the edge of the dock is approximately 8.4 m/s.