Q: A water polo player throws a ball at an angle of $$70.0^\circ$$ with an initial velocity of $$12.0\ \mathrm{m/s}. $$What is the initial vertical component of the velocity?

$$v_{0y} = 12.0 \times \sin(70.0^\circ) = 11.3\ \mathrm{m/s}$$

Q: How long is the ball in the air? (Ignore air resistance, $$g = 9.8\ \mathrm{m/s^2$}$$, $$v_{0y} = 11.3\ \mathrm{m/s})$$

$$t = \frac{2v_{0y}}{g} = \frac{2 \times 11.3}{9.8} = 2.31\ \mathrm{s}$$

Q: What is the horizontal (x-axis) position of the ball when it reaches the other player? ($$v_{0x} = 4.10\ \mathrm{m/s}$$, $$t = 2.31\ \mathrm{s})$$

$$x = v_{0x} t = 4.10 \times 2.31 = 9.47\ \mathrm{m}$$

Q: A ball is thrown at $$70.0^\circ$$ with $$12.0\ \mathrm{m/s}. $$What is the range formula for this projectile motion?

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

Question 1

A water polo player throws a ball at an angle of $$70.0^\circ$$ with an initial velocity of $$12.0\ \mathrm{m/s}. $$What is the initial vertical component of the velocity?

Accepted Answer

$$v_{0y} = 12.0 	imes \sin(70.0^\circ) = 11.3\ \mathrm{m/s}$$

Question 2

How long is the ball in the air? (Ignore air resistance, $$g = 9.8\ \mathrm{m/s^2$}$$, $$v_{0y} = 11.3\ \mathrm{m/s})$$

Accepted Answer

$$t = \frac{2v_{0y}}{g} = \frac{2 	imes 11.3}{9.8} = 2.31\ \mathrm{s}$$

Question 3

What is the horizontal (x-axis) position of the ball when it reaches the other player? ($$v_{0x} = 4.10\ \mathrm{m/s}$$, $$t = 2.31\ \mathrm{s})$$

Accepted Answer

$$x = v_{0x} t = 4.10 	imes 2.31 = 9.47\ \mathrm{m}$$

Question 4

What is the acceleration of the ball at its maximum height?

Accepted Answer

$$a = -9.8\ \mathrm{m/s^2$}$$\ (downward, due to gravity)

Question 5

At maximum height, what are the x and y components of the velocity?

Accepted Answer

$$v_x = 4.10\ \mathrm{m/s},\ v_y = 0\ \mathrm{m/s}$$

Question 6

Which of the following best describes the velocity vector when the ball leaves the player’s hand?

Accepted Answer

The velocity vector points upward and forward at $$70.0^\circ$$ above the horizontal.

Question 7

Which of the following best describes the acceleration vector at all points during the ball’s flight (ignoring air resistance)?

Accepted Answer

The acceleration vector always points straight downward with magnitude $$9.8\ \mathrm{m/s^2$}.$$

Question 8

If the ball is thrown with the same speed but at a lower angle, what happens to the time the ball spends in the air?

Accepted Answer

The time in the air decreases.

Question 9

If the ball is thrown with the same speed but at a lower angle, what happens to the horizontal distance traveled?

Accepted Answer

The horizontal distance may increase, reach a maximum, then decrease as the angle decreases.

Question 10

Which equation would you use to find the maximum height reached by the ball?

Accepted Answer

$$h_{max} = \frac{v_{0y}^2}{2g}$$

Question 11

A ball is thrown at $$70.0^\circ$$ with $$12.0\ \mathrm{m/s}. $$What is the range formula for this projectile motion?

Accepted Answer

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

Question 12

If air resistance is not ignored, which of the following is true about the ball’s motion?

Accepted Answer

The range and maximum height would both decrease.

Question 13

Which of the following is a correct expression for the vertical position $$y as a $$function of time $$t$$ for this projectile?

Accepted Answer

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

Question 14

At the instant the ball reaches the other player’s hand, what is the vertical component of its velocity?

Accepted Answer

$$v_y = -v_{0y}$$

Question 15

Which of the following best describes the path of the ball?

Accepted Answer

A parabola

Projectile Motion: Water Polo Ball Throw

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