Question

A child operating a radio-controlled model car on a dock accidentally steers it off the edge. The car's displacement 0.7 s after leaving the dock has a magnitude of 10.0 m. What is the car's speed at the instant it drives off the edge of the dock?

Answer 1

To find the car's initial speed, the problem was broken down into finding vertical displacement due to gravity, then calculating horizontal displacement using the Pythagorean theorem. The initial horizontal speed was then determined by dividing horizontal displacement by time, resulting in approximately 13.86 m/s.

Step-by-step explanation:

The question asks for the initial speed of a radio-controlled model car as it drives off a dock, given that its displacement is 10.0 m after 0.7 s. To solve this, we can use the equations of motion under constant acceleration due to gravity ('g' = 9.8 m/s²), as the car is falling freely after leaving the edge.

First, we can find the vertical component of the displacement caused by gravity using the formula:

s = ut + (1/2)gt²

Since the initial vertical speed (u) is 0 (as it just begins to fall off the dock), the equation simplifies to:

s = (1/2)gt²

Plugging in the values: s = (1/2)(9.8 m/s²)(0.7 s)² = 2.408 m

Now, we know the vertical displacement, we can find the horizontal component of the displacement using Pythagoras theorem, assuming the total displacement formed a right triangle with horizontal and vertical components:

Horizontal displacement = √(total displacement)² - (vertical displacement)²
= √(10.0 m)² - (2.408 m)²
= √100 - 5.798
= √94.202
= 9.705 m

The horizontal speed remains constant since there is no horizontal acceleration. Hence, the horizontal displacement divided by time gives us the initial speed:

Speed = horizontal displacement / time
= 9.705 m / 0.7 s
= 13.864 m/s

Thus, the car's initial speed was approximately 13.86 m/s at the instant it drove off the dock.