Q: Suppose a rock is dropped from rest at a location where the local acceleration due to gravity is $$9.78\ \mathrm{m/s^2$}. $$How long will it take to fall $$20\ \mathrm{m}$$? Use $$x = \frac{1}{2}gt^2$.

$$t = \sqrt{\frac{2x}{g}} = \sqrt{\frac{2 \times 20}{9.78}} \approx 2.02\ \mathrm{s}$$

Q: A ball is thrown straight up from the surface of the ocean (as shown in the map) with an initial velocity of $$15\ \mathrm{m/s}. $$Ignoring air resistance, what is the maximum height it reaches? Use $$v_f^2$ = v_i^2$ + 2a\Delta x$$ with $$v_f = 0$$ and $$a = -g.$$

$$\Delta x = \frac{v_i^2$}{2g} = \frac{15^2$}{2 \times 9.8} \approx 11.5\ \mathrm{m}$$

Question 1

The image above is a gravity map of Earth's oceans. What does the coloration on this map most likely represent?

Accepted Answer

Variations in the value of the acceleration due to gravity across Earth's surface

Question 2

Which of the following statements best explains why the acceleration due to gravity varies slightly across Earth's surface, as shown in the image?

Accepted Answer

Variations in Earth's density and topography cause small changes in the local gravitational field.

Question 3

If a satellite uses data from a map like the one shown to calculate the acceleration due to gravity at a specific location, which value should it use for the average acceleration due to gravity near Earth's surface?

Accepted Answer

$$g = 9.8\ \mathrm{m/s^2$}$$

Question 4

Suppose a rock is dropped from rest at a location where the local acceleration due to gravity is $$9.78\ \mathrm{m/s^2$}. $$How long will it take to fall $$20\ \mathrm{m}$$? Use $$x = \frac{1}{2}gt^2$.

Accepted Answer

$$t = \sqrt{\frac{2x}{g}} = \sqrt{\frac{2 	imes 20}{9.78}} \approx 2.02\ \mathrm{s}$$

Question 5

Why is it reasonable to ignore air resistance for a heavy object dropped from a moderate height, as discussed in the study materials?

Accepted Answer

Air resistance has a negligible effect on heavy objects over short distances.

Question 6

If the positive $$x-$$axis points upward, what is the sign of the acceleration due to gravity for a freely falling object?

Accepted Answer

Negative, $$a_x = -g$$

Question 7

A ball is thrown straight up from the surface of the ocean (as shown in the map) with an initial velocity of $$15\ \mathrm{m/s}. $$Ignoring air resistance, what is the maximum height it reaches? Use $$v_f^2$ = v_i^2$ + 2a\Delta x$$ with $$v_f = 0$$ and $$a = -g.$$

Accepted Answer

$$\Delta x = \frac{v_i^2$}{2g} = \frac{15^2$}{2 	imes 9.8} \approx 11.5\ \mathrm{m}$$

Question 8

Which of the following best describes the effect of Earth's gravity variations on satellite orbits, as inferred from the map?

Accepted Answer

Small variations in gravity can cause satellites to experience slight changes in their orbits over time.

Question 9

If a feather and a stone are dropped simultaneously in a vacuum at a location shown on the map, what will happen?

Accepted Answer

Both will fall at the same rate and hit the ground at the same time.

Question 10

Suppose you are designing an experiment to measure $$g at $$different locations shown on the map. Which method would provide the most accurate results?

Accepted Answer

Drop an object from a known height and measure the time it takes to fall, then use $$g = \frac{2h}{t^2$}.$$

Chapter 3: Acceleration – Structured Study Notes

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