Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the formula for its range (horizontal distance traveled) on level ground (neglecting air resistance)?

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

Question 1

A ball is thrown horizontally from the top of a tower and another ball is dropped from the same height at the same instant. Neglecting air resistance, which ball hits the ground first?

Accepted Answer

Both balls hit the ground at the same time.

Question 2

Which of the following best describes a vector quantity?

Accepted Answer

10 m/s to the north

Question 3

An airplane is flying north at $$80\ \mathrm{km/h}$$ and encounters a crosswind blowing east at $$60\ \mathrm{km/h}. $$What is the resultant speed of the airplane relative to the ground?

Accepted Answer

$$100\ \mathrm{km/h}$$

Question 4

A projectile is launched at an angle into the air. Neglecting air resistance, what is its vertical acceleration?

Accepted Answer

$$g$$ downward

Question 5

A ball is launched at $$45^\circ to $$the horizontal. What can be said about its initial velocity components?

Accepted Answer

The horizontal and vertical components are equal.

Question 6

Which of the following statements about projectile motion is correct?

Accepted Answer

The vertical and horizontal components of motion are independent.

Question 7

A projectile is launched at $$30^\circ$$ and another at $$60^\circ$$ with the same speed. Neglecting air resistance, how do their ranges compare?

Accepted Answer

Both projectiles have the same range.

Question 8

What is the shape of the path (trajectory) of a projectile near the Earth's surface when air resistance is negligible?

Accepted Answer

A parabola

Question 9

If a projectile is launched horizontally from a height, what is its initial vertical velocity?

Accepted Answer

Zero

Question 10

A vector of magnitude 3 units is perpendicular to a vector of magnitude 4 units. What is the magnitude of their resultant?

Accepted Answer

$$5$$ units

Question 11

A ball is rolled off a table with a horizontal velocity of $$2\ \mathrm{m/s}. If $$the table is $$1.25\ \mathrm{m}$$ high, how far from the base of the table will the ball land? (Take $$g = 10\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.0\ \mathrm{m}$$

Question 12

Which of the following is true about the speed of a projectile at the top of its path (neglecting air resistance)?

Accepted Answer

It is equal to the horizontal component of velocity.

Question 13

A projectile is launched at an angle. What is its horizontal acceleration (neglecting air resistance)?

Accepted Answer

Zero

Question 14

A ball is thrown with an initial velocity $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the time to reach maximum height?

Accepted Answer

$$\frac{v_0$ \sin 	heta}{g}$$

Question 15

A projectile is launched at $$20\ \mathrm{m/s} at an $$angle of $$45^\circ. $$What is the horizontal component of its initial velocity?

Accepted Answer

$$20 \cos 45^\circ = 14.1\ \mathrm{m/s}$$

Question 16

Which of the following best describes the effect of air resistance on a projectile?

Accepted Answer

It causes the projectile to fall below the idealized parabolic path.

Question 17

A projectile is launched and lands at the same height. What is true about the time to reach maximum height and the time to return to the ground?

Accepted Answer

The time to go up equals the time to come down.

Question 18

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the formula for its range (horizontal distance traveled) on level ground (neglecting air resistance)?

Accepted Answer

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

Projectile Motion: Physics with Calculus Study Notes

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