Q: A penguin jumps horizontally off an ice ledge with a velocity of $$2\ \mathrm{m/s}. If $$the ledge is $$1.25\ \mathrm{m}$$ above the water, how long does it take for the penguin to hit the water? (Use $$g = 9.8\ \mathrm{m/s}^2)$$

$$t = \sqrt{\frac{2 \times 1.25}{9.8}} \approx 0.505\ \mathrm{s}$$

Question 1

The image shows a sequence of penguins jumping out of the water and onto the ice. Which of the following best describes how a motion diagram could be used to represent the movement of a single penguin in this scenario?

Accepted Answer

A motion diagram would show a series of dots at equal time intervals along the penguin's path, illustrating changes in position and velocity.

Question 2

If you were to mathematically describe the motion of a penguin leaping out of the water, which of the following equations would best represent its vertical position $$y as a $$function of time $$t$$, assuming constant acceleration due to gravity and an initial upward velocity $$v_0$$?

Accepted Answer

$$y = y_0$ + v_0$ t - \frac{1}{2} g t^2$

Question 3

Which of the following statements best explains why the penguin's path in the air is curved rather than straight?

Accepted Answer

The penguin's motion is influenced by both its initial velocity and the constant acceleration due to gravity, resulting in a parabolic trajectory.

Question 4

Suppose a penguin jumps with an initial velocity of $$5\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the initial vertical component of its velocity?

Accepted Answer

$$v_{0y} = 5 \sin 30^\circ = 2.5\ \mathrm{m/s}$$

Question 5

If the time between each dot in a motion diagram is $$0.2$$ seconds, and the distance between consecutive dots increases, what does this indicate about the penguin's motion?

Accepted Answer

The penguin is speeding up.

Question 6

A penguin jumps straight up from the ice with an initial velocity $$v_0. $$Ignoring air resistance, what is the velocity of the penguin at the highest point of its jump?

Accepted Answer

$$0\ \mathrm{m/s}$$

Question 7

Which of the following best describes the difference between a movie of the penguin's jump and a motion diagram of the same event?

Accepted Answer

A movie shows continuous motion, while a motion diagram represents the position of the penguin at discrete time intervals.

Question 8

If a penguin's horizontal velocity is $$3\ \mathrm{m/s}$$ and its vertical velocity is $$4\ \mathrm{m/s} at a $$certain instant, what is the magnitude of its total velocity?

Accepted Answer

$$5\ \mathrm{m/s}$$

Question 9

A student draws a motion diagram for a penguin sliding on ice and notices that the dots are equally spaced. What does this indicate about the penguin's motion?

Accepted Answer

The penguin is moving at a constant velocity.

Question 10

Which mathematical description would best model the horizontal position $$x of a $$penguin moving at a constant velocity $$v$$ starting from $$x_0$$?

Accepted Answer

$$x = x_0$ + v t$$

Question 11

If a penguin jumps at an angle and lands back on the ice at the same height from which it jumped, which of the following is true about the time it spends rising versus falling?

Accepted Answer

The time rising is equal to the time falling.

Question 12

A penguin jumps horizontally off an ice ledge with a velocity of $$2\ \mathrm{m/s}. If $$the ledge is $$1.25\ \mathrm{m}$$ above the water, how long does it take for the penguin to hit the water? (Use $$g = 9.8\ \mathrm{m/s}^2)$$

Accepted Answer

$$t = \sqrt{\frac{2 	imes 1.25}{9.8}} \approx 0.505\ \mathrm{s}$$

Describing Motion: Visualizing and Mathematically Representing Motion

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