Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the time of flight until it returns to the same vertical level? (Neglect air resistance, $$g is $$acceleration due to gravity.)

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

Question 1

A ball is thrown vertically upward with an initial velocity $$v_0$$ from ground level. It returns to its starting point after 6.0 s. Neglecting air resistance, what was the initial velocity $$v_0$$? (Take $$g = -10\ \mathrm{m/s^2$}$$, upward is positive.)

Accepted Answer

$$v_0 = 30$$\ \mathrm{m/s}$$

Question 2

A skydiver jumps from a helicopter and accelerates downward. As her speed increases, what happens to her acceleration, and why?

Accepted Answer

Her acceleration decreases because air resistance increases with speed, reducing the net force.

Question 3

Two balls are released from the same height at the same time: one is dropped vertically, and the other is thrown horizontally. Neglecting air resistance, which statement is correct?

Accepted Answer

Both balls hit the ground at the same time.

Question 4

A stone is thrown downward from a bridge with an initial speed of $$5\ \mathrm{m/s}. $$What is its speed after 2 seconds? (Take $$g = 10\ \mathrm{m/s^2$}$$, neglect air resistance.)

Accepted Answer

$$v = 25\ \mathrm{m/s}$$

Question 5

A ball is thrown straight up. At the highest point of its trajectory (neglecting air resistance), which of the following is true?

Accepted Answer

The velocity is zero, but the acceleration is $$-g.$$

Question 6

A projectile is launched horizontally from a cliff. Which statement best describes its motion?

Accepted Answer

The horizontal velocity remains constant, while the vertical velocity increases due to gravity.

Question 7

A car travels from city A to city B at $$40\ \mathrm{mph}$$ and returns at $$60\ \mathrm{mph}. $$What is the average speed for the round trip?

Accepted Answer

$$48\ \mathrm{mph}$$

Question 8

Which of the following best describes the area under a velocity-time graph?

Accepted Answer

It represents the displacement of the object.

Question 9

A position-time graph shows a straight line with a negative slope. What does this indicate about the object's motion?

Accepted Answer

The object is moving in the negative direction with constant velocity.

Question 10

A ball is thrown upward with velocity $$v_0. $$Ignoring air resistance, what is the velocity of the ball when it returns to its starting point?

Accepted Answer

It is $$-v_0$ (equal in magnitude but opposite in direction to the initial velocity).

Question 11

A cyclist rides with a constant positive velocity, then stops for a while, and finally rides back with a constant negative velocity. Which segment of the position-time graph has zero slope?

Accepted Answer

The segment where the cyclist is stopped.

Question 12

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the time of flight until it returns to the same vertical level? (Neglect air resistance, $$g is $$acceleration due to gravity.)

Accepted Answer

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

Question 13

A ball is dropped from a height $$h$$ and another is thrown upward from the same height with speed $$v_0. $$Neglecting air resistance, which statement is true about their speeds when they hit the ground?

Accepted Answer

Both balls hit the ground with the same speed.

Question 14

Which of the following equations gives the vertical displacement $$y of a $$projectile launched with initial vertical velocity $$v_{0y}$$ after time $$t$$? (Neglect air resistance.)

Accepted Answer

$$y = v_{0y} t - \dfrac{1}{2} g t^2$

Question 15

A velocity-time graph for an object shows a straight line with a positive slope. What does this indicate?

Accepted Answer

The object is accelerating at a constant rate.

Question 16

A ball is thrown downward from a tall building with an initial speed of $$10\ \mathrm{m/s}. $$How far does it fall in 3 seconds? (Take $$g = 10\ \mathrm{m/s^2$}$$, neglect air resistance.)

Accepted Answer

$$75\ \mathrm{m}$$

Question 17

Which of the following best describes the acceleration of a freely falling object near Earth's surface (neglecting air resistance)?

Accepted Answer

It is constant and directed downward.

Question 18

A position-time graph is a straight horizontal line. What does this indicate about the object's motion?

Accepted Answer

The object is at rest.

Question 19

A projectile is launched at $$20\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the initial vertical component of its velocity?

Accepted Answer

$$v_{0y} = 10\ \mathrm{m/s}$$

Question 20

A ball is thrown straight up and reaches a maximum height of $$20\ \mathrm{m}. $$What was its initial velocity? (Take $$g = 10\ \mathrm{m/s^2$}$$, neglect air resistance.)

Accepted Answer

$$v_0 = 20$$\ \mathrm{m/s}$$

Kinematics: Freely Falling Bodies and Graphical Analysis

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