Q: A body initially travels at $$20\,\mathrm{m/s}$$ westward. Two seconds later, the body is found traveling at $$20\,\mathrm{m/s}$$ northward. Find the average acceleration of the body during the two seconds.

$$14\,\mathrm{m/s^2$}$$\,\text{north-eastward}$

Q: If you want your weight to be $$\frac{1}{2} of $$your normal weight, what is the acceleration?

$$\frac{g}{2}$$\,\text{downwards}

Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the range of the projectile on level ground?

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

Question 1

A ball is launched vertically upward so that it reaches a height of $$20\,\mathrm{m}. $$What initial speed should you launch the ball? Assume no air resistance and $$g = 10\,\mathrm{m/s^2$}.$$

Accepted Answer

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

Question 2

A body initially travels at $$20\,\mathrm{m/s}$$ westward. Two seconds later, the body is found traveling at $$20\,\mathrm{m/s}$$ northward. Find the average acceleration of the body during the two seconds.

Accepted Answer

$$14\,\mathrm{m/s^2$}$$\,	ext{north-eastward}$

Question 3

A boatman tries to row across a river so that the boat arrives at the opposite shore directly across from the starting point. The river flows at a velocity $$2.0\,\mathrm{m/s}$$ downstream. The boat can row at a speed $$1.0\,\mathrm{m/s}. In $$what direction should the boatman row the boat?

Accepted Answer

The boat necessarily arrives downstream of the opposite shore directly across from the starting point no matter in which direction he rows the boat because the flow of the river is too fast.

Question 4

From the top of a building two balls are thrown at the same time at identical speed: Ball A is thrown at an angle $$	heta$$ above the horizontal, and Ball B is thrown at an angle $$	heta$$ below the horizontal. (i) Which ball hits the ground first? (ii) Which ball hits the ground with faster speed? (Air resistance is negligible.)

Accepted Answer

(i) B, (ii) tie

Question 5

An apple and a melon, which is twice as massive as the apple, are dropped at the same time and they hit the ground at the same time. This is because...

Accepted Answer

Earth pulls the melon with twice the amount of pull making them accelerate at the same rate.

Question 6

A skydiver is falling toward the ground, but due to air resistance the fall is at constant velocity. What is the interaction pair (of Newton's 3rd law) of the gravitational force acting on the skydiver?

Accepted Answer

the gravitational force with which the skydiver pulls up the Earth

Question 7

If you want your weight to be $$\frac{1}{2} of $$your normal weight, what is the acceleration?

Accepted Answer

$$\frac{g}{2}$$\,	ext{downwards}

Question 8

Two blocks are connected by a massless rope and a massless pulley as in the picture. Block 1 (mass $$m_1) on a $$frictionless $$30^\circ$$ ramp is twice as massive as Block 2 (mass $$m_2) $$hanging vertically. At one moment Block 1 is found sliding up the ramp, while Block 2 is going down. What will happen to the motion a moment later? The rope is always taut (i.e., never slack) and its length remains fixed.

Accepted Answer

Block 1 slows down; Block 2 slows down

Question 9

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the range of the projectile on level ground?

Accepted Answer

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

Question 10

A car travels $$100\,\mathrm{km}$$ north in $$2\,\mathrm{h}$$, then $$100\,\mathrm{km}$$ east in $$2\,\mathrm{h}. $$What is the magnitude of the average velocity?

Accepted Answer

$$70.7\,\mathrm{km/h}$$

Midterm 1

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