Q: A projectile is launched at speed $$v_0$$ and angle $$\theta$$ above the horizontal. What is the formula for its range $$R ($$horizontal distance traveled before landing)?

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

Question 1

A car traveling at $$v_0 = 27$$\ \mathrm{m/s}$$ must stop at a red light 180$$\ \mathrm{m}$$ ahead. What is the required constant acceleration a$ to stop exactly at the light?

Accepted Answer

$$a = -\dfrac{v_0$^2}{2(x_1$ - x_0$)}$$

Question 2

Which of the following correctly expresses the position $$x as a $$function of time for an object moving in one dimension with constant acceleration $$a$$ and initial velocity $$v_0$$?

Accepted Answer

$$x = \dfrac{1}{2} a t^2$ + v_0$ t + x_0$

Question 3

A ball is thrown straight up with initial velocity $$v_0. $$What is the maximum height $$h it $$reaches?

Accepted Answer

$$h = \dfrac{v_0$^2}{2g}$$

Question 4

An object moves with constant acceleration $$a. $$Which equation relates its final velocity $$v to $$its initial velocity $$v_0$$, acceleration $$a$$, and displacement $$x - x_0$?

Accepted Answer

$$v^2$$ = $$v_0^2 + 2a(x$$ - $$x_0$$)$$

Question 5

Achilles and the tortoise are racing. Achilles runs at $$v_A$$, the tortoise at $$v_t$$, and the tortoise has a head start of $$x_0. $$How long does it take Achilles to catch up?

Accepted Answer

$$t_1$$ = \dfrac{$$x_0$$}{v_A - v_t}$$

Question 6

A ball is dropped from a height $$h. $$How long does it take to reach the ground?

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}}$$

Question 7

A projectile is launched at speed $$v_0$$ and angle $$	heta$$ above the horizontal. What is the formula for its range $$R ($$horizontal distance traveled before landing)?

Accepted Answer

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

Question 8

A bulldozer moves at $$45^\circ to $$the left with respect to a moving sheet. If the sheet moves to the right at $$v_s$$ and the bulldozer moves at $$v_p$$ relative to the sheet, what is the bulldozer's velocity with respect to the ground?

Accepted Answer

$$\vec{v}_{bg} = \vec{v}_s + \vec{v}_p$$

Question 9

Which of the following statements about acceleration is correct?

Accepted Answer

Acceleration occurs whenever velocity changes, regardless of direction.

Question 10

A ball is thrown straight up with initial velocity $$v_0. $$What is its velocity when it returns to the starting point?

Accepted Answer

$$-v_0$

Question 11

An object moves in the negative $$x-$$direction and its velocity is becoming more negative over time. What can you say about its acceleration?

Accepted Answer

The acceleration is negative.

Question 12

A ball is thrown horizontally from a cliff of height $$h$$ with initial speed $$v_0. $$How far from the base of the cliff does it land?

Accepted Answer

$$x = v_0$ \sqrt{\dfrac{2h}{g}}$$

Question 13

Which of the following is the correct expression for the $$x-$$component of a vector of magnitude $$r at $$angle $$	heta$$ from the positive $$x-$$axis?

Accepted Answer

$$x = r \cos 	heta$$

Question 14

A car is braking with constant acceleration. If its initial velocity is $$v_0$$ and it comes to rest after traveling distance $$d$$, what is the magnitude of its acceleration?

Accepted Answer

$$a = \dfrac{v_0$^2}{2d}$$

Question 15

In projectile motion, which component of velocity remains constant (ignoring air resistance)?

Accepted Answer

Horizontal component

Question 16

A ball is thrown upward and caught at the same height. What is the total time in the air if its initial velocity is $$v_0$$?

Accepted Answer

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

Question 17

A bulldozer crosses several moving sheets with combined width $$L$$ and vertical velocity $$v_y. $$What is the time to cross all sheets?

Accepted Answer

$$t = \dfrac{L}{v_y}$$

Question 18

Which of the following is true about motion in two dimensions?

Accepted Answer

Motion in $$x$$ and $$y is $$independent, but linked through time.

Question 19

A car moves at $$v_A$$ and another at $$v_t in $$the same direction. What is their relative velocity?

Accepted Answer

$$v_A - v_t$$

Physics 211: Kinematics and Reference Frames – Midterm 1 Review Study Notes

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