Q: A ball is thrown at speed $$11.2 m/s at an $$angle $$35^\circ$$ above the horizontal. How long does it take before the projectile returns to the ground? (Assume $$g = 9.8 m/s$^2)$$

$$t = \frac{2v_0 \sin \theta}{g}$$

Q: A projectile is launched from the ground with initial speed $$v_0 at $$angle $$\theta. $$What is the range $$R of $$the projectile?

$$R = \frac{v_0$^2 \sin 2\theta}{g}$$

Question 1

A car moves along a straight road with a velocity that changes as shown in the graph below. The area under the velocity-time graph between $$t = 0$$ and $$t = 5 s is $$shaded. What does this area represent?

Accepted Answer

The car's displacement over the interval

Question 2

A projectile is shot at some angle $$	heta$$ ($$0 \u003c 	heta \u003c 90^\circ) $$relative to the horizontal. Which of the following statements is TRUE at the moment the projectile reaches its maximum vertical height?

Accepted Answer

Its vertical velocity is zero, and its horizontal velocity is unchanged from launch.

Question 3

A student throws a ball upward with an initial speed $$v_0$$ from the edge of a building of height $$h. $$Neglecting air resistance, what is the speed of the ball just before it hits the ground?

Accepted Answer

$$\sqrt{v_0$^2 + 2gh}$$

Question 4

Two people, A and B, are walking westwards to an airport. A walks on a moving walkway at speed $$v$$ relative to the walkway, while B walks on the ground at the same speed $$v. $$The walkway moves west at speed $$w. If $$both walk the same distance $$L$$, who arrives first?

Accepted Answer

Person A, because their effective speed is $$v + w$$

Question 5

A ball is thrown at speed $$11.2 m/s at an $$angle $$35^\circ$$ above the horizontal. How long does it take before the projectile returns to the ground? (Assume $$g = 9.8 m/s$^2)$$

Accepted Answer

$$t = \frac{2v_0 \sin 	heta}{g}$$

Question 6

A particle moves in the $$xy-$$plane with position $$\vec{r}(t) = (4t)\hat{i} + (9 - 4t^2$)\hat{j}. At $$what time $$t$$ does the particle reach its maximum $$y-$$coordinate?

Accepted Answer

$$t = 2 s$$

Question 7

A boat must cross a river flowing east at $$5 m/s. $$The boat can travel at $$4 m/s $$relative to the water. What is the minimum time to cross the river if the width is $$100 m$$?

Accepted Answer

$$t = \frac{100}{4} s$$

Question 8

A projectile is launched from the ground and reaches a maximum height $$h. $$What is the initial vertical velocity $$v_{0y}$$ required to reach this height?

Accepted Answer

$$v_{0y} = \sqrt{2gh}$$

Question 9

A student analyzes a friend's homework and finds the following vector addition: $$[A] + [B] = [C]. If$$ $$|A| = 5$$ and $$|B| = 3$$, which of the following could be the magnitude of $$C$$?

Accepted Answer

$$|C| = 2$$

Question 10

A projectile is launched from point A and lands at point C, passing over a building at point B. If the projectile's initial speed is $$v_0$$ and launch angle is $$	heta$$, what is the horizontal component of its velocity as it passes over the building?

Accepted Answer

$$v_0$$ \cos 	heta$$

Question 11

A car accelerates uniformly from rest to a speed of $$20 m/s in$$ $$5$$ seconds. What is its acceleration?

Accepted Answer

$$a = 4 m/s$^2$$

Question 12

A ball is dropped from a height $$h$$ and takes $$t$$ seconds to reach the ground. What is the value of $$h in $$terms of $$t$$ and $$g$$?

Accepted Answer

$$h = \frac{1}{2}gt^2$

Question 13

A projectile is launched from the ground with initial speed $$v_0 at $$angle $$	heta. $$What is the range $$R of $$the projectile?

Accepted Answer

$$R = \frac{v_0$^2 \sin 2	heta}{g}$$

Question 14

A person walks east at $$3 m/s on a $$walkway moving east at $$2 m/s. $$What is the person's speed relative to the ground?

Accepted Answer

$$5 m/s$

Question 15

A ball is thrown horizontally from a height $$h$$ with speed $$v_0. $$How long does it take to hit the ground?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}}$$

Question 16

A car travels $$120 m in$$ $$5 s. $$What is its average velocity?

Accepted Answer

$$24 m/s$

Question 17

A projectile is launched from the ground and lands at the same height. If the time of flight is $$T$$, what is the initial vertical velocity?

Accepted Answer

$$v_{0y} = \frac{gT}{2}$$

Question 18

A person walks west at $$2 m/s on a $$walkway moving east at $$3 m/s. $$What is the person's speed relative to the ground?

Accepted Answer

$$1 m/s$ $$ east

Kinematics and Projectile Motion: Study Notes and Worked Examples

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