Q: A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. Neglecting air resistance, what is the formula for the range $$R of $$the projectile?

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

Q: A ball is thrown at an angle $$\theta$$ with initial speed $$v_0. $$What is the time of flight until it returns to the same vertical level?

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

Question 1

You are going to throw a ball along some angle above the horizontal. To throw it as far as possible, you should:

Accepted Answer

run in the direction you're throwing the ball, and throw it with the highest speed you can.

Question 2

A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Neglecting air resistance, what is the formula for the range $$R of $$the projectile?

Accepted Answer

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

Question 3

If you throw a ball at an angle of $$45^\circ$$ with respect to the horizontal, which of the following statements is true (neglecting air resistance)?

Accepted Answer

The ball will reach its maximum range.

Question 4

A soccer player kicks a ball with an initial velocity of $$20\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the initial horizontal component of the velocity?

Accepted Answer

$$20 \cos 30^\circ$$

Question 5

A runner throws a ball forward while running at $$5\ \mathrm{m/s}$$ and throws the ball at $$15\ \mathrm{m/s}$$ relative to herself. What is the speed of the ball relative to the ground?

Accepted Answer

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

Question 6

Which of the following best explains why running in the same direction as you throw a ball increases its range?

Accepted Answer

Your running speed adds to the ball's initial velocity, increasing the total horizontal velocity.

Question 7

If you throw a ball straight up while running forward, what will be the path of the ball as seen by an observer standing still?

Accepted Answer

A parabolic arc.

Question 8

A baseball is thrown horizontally from a cliff with a speed of $$10\ \mathrm{m/s}. $$How far from the base of the cliff will the ball land after $$2$$ seconds?

Accepted Answer

$$20\ \mathrm{m}$$

Question 9

Which of the following is true about the vertical and horizontal motions of a projectile (neglecting air resistance)?

Accepted Answer

They are independent of each other.

Question 10

A ball is thrown at an angle $$	heta$$ with initial speed $$v_0. $$What is the time of flight until it returns to the same vertical level?

Accepted Answer

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

Question 11

A person throws a ball at $$10\ \mathrm{m/s} at an $$angle of $$60^\circ$$ above the horizontal. What is the vertical component of the initial velocity?

Accepted Answer

$$10 \sin 60^\circ$$

Question 12

If a projectile is launched and lands at the same height, which of the following pairs of launch angles will result in the same range (assuming the same initial speed)?

Accepted Answer

$$30^\circ$$ and $$60^\circ$$

Projectile Motion and Maximizing Range

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