A hiker stands on the edge of a cliff 490 m above the ground and throws a stone horizontally with an initial speed of 15 m/s. Neglecting air resistance, the time taken by the stone to reach the ground and the speed with which it hits the ground are, respectively: (Take g = 9.8 $\mathrm{m}/{\mathrm{s}}^2$ ).

1.  10 s & 99 m/s

2.  10 s & 15 m/s

3.  5 s & 99 m/s

4.  5 s & 15 m/s

A cricket ball is thrown at a speed of 28 m/s in a direction 30° above the horizontal. The time taken by the ball to return to the same level is:

An insect trapped in a circular groove of radius 12 cm moves along the groove steadily and completes 7 revolutions in 100 s. What is the angular speed of the motion? 

1.  0.62 rad/s

2.  0.06 rad/s

3.  4.40 rad/s

4.  0.44 rad/s

An insect trapped in a circular groove of radius 12 cm moves along the groove steadily and completes 7 revolutions in 100 s. Is the acceleration vector a constant vector? What is its magnitude?

1.  yes, 2.3 $\mathrm{cm}/{\mathrm{s}}^2$

2.  no, 5.3 $\mathrm{cm}/{\mathrm{s}}^2$

3.  yes, 5.3 $\mathrm{cm}/{\mathrm{s}}^2$

4.  no, 2.3 $\mathrm{cm}/{\mathrm{s}}^2$

A cricket ball is thrown at a speed of 28 m/s in a direction 30° above the horizontal. The maximum height attained by the ball is:

1.  5 m

2.  10 m

3.  15 m

4.  20 m

Galileo, in his book Two new sciences, stated that for elevations that exceed or fall short of 45° by equal amounts, the ranges?

1.  are equal to each other.

2.  are not equal to each other.

3.  are sometimes equal and sometimes are not equal to each other.

4. it depends on the difference between the angles.

Rain is falling vertically with a speed of 35 m/s. A woman rides a bicycle with a speed of 12 m/s in the east to west direction. What is the direction in which she should hold her umbrella?

1.  In the vertical direction only

2.  $19°$ with vertical towards east

3.  $19°$ with vertical towards the west

4.  $19°$ with vertical towards the south

A particle starts from the origin at t = 0 with a velocity of 5.0î m/s and moves in the x-y plane under the action of a force that produces a constant acceleration of (3.0î +2.0 ĵ ) $\mathrm{m}/{\mathrm{s}}^2$. What is the speed of the particle at the instant its x-coordinate is 84 m?

1.  36 m/s 

2.  26 m/s

3.  1 m/s

4.  0 m/s

The position of a particle is given by $\overrightarrow{\mathrm{r} }= \left(3.0\mathrm{t} \hat{\mathrm{i}} - 2.0{\mathrm{t}}^2 \hat{\mathrm{j}} +4.0 \hat{\mathrm{k}}\right) \mathrm{m}$ where t is in seconds and the coefficients have the proper units for r to be in meters. The magnitude and direction of $\overrightarrow{\mathrm{v}\left(\mathrm{t}\right)}$ at t = 1.0 s are:

1.  4 m/s at ${53}^o$ with x-axis

2.  4 m/s at ${37}^o$ with x-axis

3.  5 m/s at ${53}^o$ with y-axis

4.  5 m/s at ${53}^o$ with x-axis

A motorboat is racing towards the north at 25 km/h and the water current in that region is 10 km/h in the direction of 60° east of the south. The resultant velocity of the boat is:

1. 12 km/h at $23.4^o$ east of west

2. 22 km/h at $23.4^o$ north of east

3. 22 km/h at $23.4^o$ east of north

4. 20 km/h at $23.4^o$ north of wast