A child operating a radio-controlled model car on a dock accidentally steers it off the edge. The car's displacement 0.58 s after leaving the dock has a magnitude of 7.1 m. What is the car's speed at the instant it drives off the edge of the dock?
What do you mean by displacement? Horizontal distance from the edge, or the actual slant distance (the resultant of vertical and horizontal components) from the edge?
I will assume the latter, since you refer to the magnitude.
In 0.58 s, the car will fall
Y = (g/2)*t^2 = 1.648 meters
The horizontal distance it will have moved is then
X = sqrt[(7.1)^2 - (1.648)^2] = 6.91 m
The car's speed at the edge would be
X/t = 6.91/0.58 = 11.9 m/s
To find the car's speed at the instant it drives off the edge of the dock, we need to use the formula for speed:
speed = displacement / time
Given that the magnitude of the car's displacement is 7.1 m and the time is 0.58 s, we can substitute these values into the formula to find the car's speed:
speed = 7.1 m / 0.58 s
To evaluate this expression, divide 7.1 by 0.58:
speed = 12.24 m/s
Therefore, the car's speed at the instant it drives off the edge of the dock is 12.24 m/s.
To find the car's speed at the instant it drives off the edge of the dock, we need to use the formula for speed, which is defined as the magnitude of the displacement divided by the time taken.
The given displacement, 7.1 m, is the magnitude of the car's displacement 0.58 s after leaving the dock. So, the magnitude of the displacement is equal to the distance the car has traveled from the dock.
To find the car's speed, we need to divide the magnitude of the displacement by the time taken. Let's plug in the values:
Speed = Magnitude of Displacement / Time
Speed = 7.1 m / 0.58 s
Dividing these values, we find:
Speed ≈ 12.24 m/s
Therefore, the car's speed at the instant it drives off the edge of the dock is approximately 12.24 m/s.