Q: A basketball is launched from the ground with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal, as shown in the diagram. Which of the following correctly gives the horizontal and vertical components of the initial velocity?

$$v_{0x} = v_0$ \cos \theta$$, $$v_{0y} = v_0$ \sin \theta$$

Q: If the basketball is launched with an initial speed $$v_0 at an $$angle $$\theta$$ and lands at the same height from which it was launched, what is the total time the ball spends in the air?

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

Q: What is the maximum height reached by the basketball during its flight?

$$h_{max} = \dfrac{v_0$^2 \sin^2$ \theta}{2g}$$

Q: Which equation gives the range $$R of $$the projectile (horizontal distance traveled) when it lands at the same height it was launched?

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

Question 1

A basketball is launched from the ground with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal, as shown in the diagram. Which of the following correctly gives the horizontal and vertical components of the initial velocity?

Accepted Answer

$$v_{0x} = v_0$ \cos 	heta$$, $$v_{0y} = v_0$ \sin 	heta$$

Question 2

If the basketball is launched with an initial speed $$v_0 at an $$angle $$	heta$$ and lands at the same height from which it was launched, what is the total time the ball spends in the air?

Accepted Answer

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

Question 3

What is the maximum height reached by the basketball during its flight?

Accepted Answer

$$h_{max} = \dfrac{v_0$^2 \sin^2$ 	heta}{2g}$$

Question 4

Which of the following statements about the projectile's velocity at the highest point of its trajectory is correct?

Accepted Answer

The velocity is entirely horizontal.

Question 5

If the launch angle $$	heta is $$increased while keeping the initial speed $$v_0$$ constant, what happens to the range of the projectile?

Accepted Answer

The range increases up to $$45^\circ$$ and then decreases.

Question 6

Which equation gives the range $$R of $$the projectile (horizontal distance traveled) when it lands at the same height it was launched?

Accepted Answer

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

Question 7

At the instant the basketball reaches its maximum height, what is the vertical component of its velocity?

Accepted Answer

$$v_{y} = 0$$

Question 8

If air resistance is neglected, which of the following best describes the acceleration of the basketball during its flight?

Accepted Answer

The acceleration is constant and points downward.

Question 9

Suppose the basketball is launched at $$30^\circ$$ with an initial speed of $$10\ \mathrm{m/s}. $$What is the initial vertical component of the velocity?

Accepted Answer

$$v_{0y} = 10 \sin 30^\circ$$

Question 10

If the basketball is launched from the ground and lands at the same height, which of the following best describes the symmetry of its trajectory?

Accepted Answer

The time to ascend equals the time to descend.

Exam 1 Review: Kinematics and Newtonian Mechanics (Chapters 1-4)

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