Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the maximum height reached by the projectile?

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

Q: A vector $$\vec{A} is $$given by $$\vec{A} = 3\hat{i} + 4\hat{j}. $$What is the direction of $$\vec{A}$$ with respect to the x-axis?

$$\tan$$^{-1}$$\left(\frac{4}{3}\right)$$

Question 1

The period of a pendulum on the planet Jupiter is being studied. If the pendulum is swung back and forth, what is the correct formula for the period $$T in $$terms of the length $$l$$ and the acceleration due to gravity $$g$$?

Accepted Answer

$$T = 2\pi \sqrt{\frac{l}{g}}$$

Question 2

A rock is dropped (from rest) from the top of a tall building. How far above the ground is the rock 1.5 seconds before it reaches the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$}$$ and neglect air resistance.)

Accepted Answer

$$h = \frac{1}{2}g(1.5)^2$

Question 3

Refer to the figure showing two vectors $$\vec{A}$$ and $$\vec{B}. $$Which of the following expressions gives the resultant vector $$\vec{R}$$?

Accepted Answer

$$\vec{R} = \vec{A} + \vec{B}$$

Question 4

A ball is thrown upward from the edge of a cliff with an initial speed of $$v_0. $$What is the time taken for the ball to reach its maximum height?

Accepted Answer

$$t = \frac{v_0$}{g}$$

Question 5

Which of the following best describes the acceleration of an object in free fall near the Earth's surface (neglecting air resistance)?

Accepted Answer

It is constant and equal to $$9.8\ \mathrm{m/s^2$}$$ downward.

Question 6

If a vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4$$, what is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5$$

Question 7

A car accelerates uniformly from rest to a speed $$v in $$time $$t. $$What is the acceleration $$a$$?

Accepted Answer

$$a = \frac{v}{t}$$

Question 8

Which of the following is a scalar quantity?

Accepted Answer

Speed

Question 9

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the maximum height reached by the projectile?

Accepted Answer

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

Question 10

A vector has a magnitude of $$10$$ units and makes an angle of $$30^\circ$$ with the x-axis. What is its x-component?

Accepted Answer

$$10 \cos 30^\circ$$

Question 11

A car travels 100 m north, then 100 m east. What is the magnitude of the displacement?

Accepted Answer

$$\sqrt{100^2$ + 100^2$}$$

Question 12

Which of the following is NOT a vector quantity?

Accepted Answer

Distance

Question 13

If the velocity of an object is constant, what can be said about its acceleration?

Accepted Answer

Acceleration is zero.

Question 14

A ball is thrown vertically upward with speed $$v_0. $$What is the total time the ball spends in the air before returning to the thrower's hand?

Accepted Answer

$$t = \frac{2v_0}{g}$$

Question 15

A vector $$\vec{A} is $$given by $$\vec{A} = 3\hat{i} + 4\hat{j}. $$What is the direction of $$\vec{A}$$ with respect to the x-axis?

Accepted Answer

$$	an$$^{-1}$$\left(\frac{4}{3}ight)$$

Physics 107 Midterm Study Guidance: Kinematics and Mechanics

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