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Chapter 3: Problem 56

By trial and error, a frog learns that it can leap a maximum horizontal distance of \(1.3 \mathrm{~m}\). If, in the course of an hour, the frog spends \(20 \%\) of the time resting and \(80 \%\) of the time performing identical jumps of that maximum length, in a straight line, what is the distance traveled by the frog?

Short Answer

Expert verified
Question: In one hour, a frog travels continuously by leaping. It spends 80% of the time leaping, with each leap having a maximum horizontal distance of 1.3 meters. Calculate the total distance traveled by the frog in one hour. Answer: The frog travels a total distance of 3744 meters.

Step by step solution

01

Calculate the amount of time spent leaping

We know that the frog spends 80% of the time leaping. Since the total time is one hour, we can find the time spent leaping by multiplying the total time by the given percentage. As a decimal, 80% is 0.8. So, the amount of time spent leaping is: \(1 \text{ hour} \times 0.8 = 0.8 \text{ hours}\)
02

Convert hours to seconds

To determine the number of leaps, we need to convert the time spent leaping in hours to seconds. There are 3600 seconds in an hour, so we can convert the time as follows: \(0.8 \text{ hours} \times 3600 \frac{\text{seconds}}{\text{hour}} = 2880 \text{ seconds}\)
03

Calculate the number of leaps

The frog performs identical jumps continuously during the time spent leaping. We are not given the duration of each leap, but we are asked to find the distance traveled in one hour. So, let's assume that the frog completes one leap per second. Thus, the number of leaps performed in the 2880 seconds is: \(2880 \text{ leaps}\)
04

Calculate the total distance traveled

Now that we know that the frog performs 2880 leaps, each with a maximum horizontal distance of 1.3 meters, we can calculate the total distance the frog travels by multiplying these values together: \(2880 \text{ leaps} \times 1.3 \frac{\text{meters}}{\text{leap}} = 3744 \text{ meters}\) Therefore, the frog travels a total distance of 3744 meters.

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Most popular questions from this chapter

A firefighter, \(60 \mathrm{~m}\) away from a burning building, directs a stream of water from a ground-level fire hose at an angle of \(37^{\circ}\) above the horizontal. If the water leaves the hose at \(40.3 \mathrm{~m} / \mathrm{s}\), which floor of the building will the stream of water strike? Each floor is \(4 \mathrm{~m}\) high.

In ideal projectile motion, when the positive \(y\) -axis is chosen to be vertically upward, the \(y\) -component of the acceleration of the object during the ascending part of the motion and the \(y\) -component of the acceleration during the descending part of the motion are, respectively, a) positive, negative. c) positive, positive. b) negative, positive. d) negative, negative.

Some rental cars have a GPS unit installed, which allows the rental car company to check where you are at all times and thus also know your speed at any time. One of these rental cars is driven by an employee in the company's lot and, during the time interval from 0 to \(10 \mathrm{~s}\), is found to have a position vector as a function of time of $$ \begin{aligned} \vec{r}(t)=&\left((24.4 \mathrm{~m})-t(12.3 \mathrm{~m} / \mathrm{s})+t^{2}\left(2.43 \mathrm{~m} / \mathrm{s}^{2}\right)\right.\\\ &\left.(74.4 \mathrm{~m})+t^{2}\left(1.80 \mathrm{~m} / \mathrm{s}^{2}\right)-t^{3}\left(0.130 \mathrm{~m} / \mathrm{s}^{3}\right)\right) \end{aligned} $$ a) What is the distance of this car from the origin of the coordinate system at \(t=5.00 \mathrm{~s} ?\) b) What is the velocity vector as a function of time? c) What is the speed at \(t=5.00 \mathrm{~s} ?\) Extra credit: Can you produce a plot of the trajectory of the car in the \(x y\) -plane?

An outfielder throws a baseball with an initial speed of \(32 \mathrm{~m} / \mathrm{s}\) at an angle of \(23^{\circ}\) to the horizontal. The ball leaves his hand from a height of \(1.83 \mathrm{~m}\). How long is the ball in the air before it hits the ground?

For a science fair competition, a group of high school students build a kicker-machine that can launch a golf ball from the origin with a velocity of \(11.2 \mathrm{~m} / \mathrm{s}\) and initial angle of \(31.5^{\circ}\) with respect to the horizontal. a) Where will the golf ball fall back to the ground? b) How high will it be at the highest point of its trajectory? c) What is the ball's velocity vector (in Cartesian components) at the highest point of its trajectory? d) What is the ball's acceleration vector (in Cartesian components) at the highest point of its trajectory?
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