What is the distance and the displacement of the race car drivers in the Indy 500?
1 answer:
You might be interested in
Answer:28.8 knots
Explanation:
The ships are moving as the sides of a right triangle. Thus, Pyhogorean theorem will be useful in the following steps. Next, we have to know that the rate of change in distance, which is called velocity, can be described in terms of derivatives.
First, we have to calculate the distances covered by the ships from noon to 6 PM. In 6 hours, ship A moved 22*6=132 nautical mile. However, their first distance was 10 nautical miles, so 132+10=142 miles is the equivalent of A's displacement. For B, the distance travelled is 19*6=114 miles. From now on, A=142 miles and B=114 miles.
The distance between them is described with Pythogorean theorem, which is and when we replace the values A and D, we find Distance (D) to be 182 miles.
Now, let's make the notations clear. The velocity of A and B is notated as and
. The rate of change of distance is also notated as
. Now, we have to find
from the Pythogorean theorem. If we derive the Pythogorean expression
, we would have:
The derivation here includes chain rule and derives the interior parts of the parenthesis. When we insert distances for A and B and velocities for derivation notations, the formula becomes:
and the answer is 28.6 knots.