Projectile Motion

For a projectile fired with a certain velocity, the maximum possible Range and the maximum height attainable are related as …

• $R_{\max}=2H_{\max}$

• $R_{\max}=\frac{H_{\max}}{2}$

• $R_{\max}=4H_{\max}$

• $R_{\max}=H_{\max}$

The angle of projection for the range of projectile to be equal to its maximum height is …

• $θ=\tanˉ¹(2)$

• $θ=\tanˉ¹(3)$

• $θ=\tanˉ¹(4)$

• $θ=\tanˉ¹(2/\sqrt{3})$

A ball is projected with velocity  $10\ m/\sec$  at angle  $30°$ of with the horizontal surface. The angle made by the line joining point of projection with the point of maximum height is …

•  $\tan^{-1}⁡\left(\frac{2}{\sqrt{3}}\right)\$

•  $\tan^{-1}⁡\left(\frac{1}{2\sqrt{3}}\right)\$

•  $\tan^{-1}⁡\left(\sqrt{3}\right)\$

•  $\tan^{-1}⁡\left(\frac{1}{\sqrt{3}}\right)\$

A ball is projected with velocity  $10\ m/\sec$  at angle of  $30\degree$  with the horizontal surface. The speed of the ball after (1 second) will be … (Use $g=10\ m⁄s^2$ )

•  $5\ m/\sec$ 

•  $20\ m/\sec$ 

•  $8\ m/\sec$ 

•  $10\ m/\sec$ 

An object is thrown upwards with a velocity of (30 m/s) near the surface of the earth. After two seconds what would be the direction of the displacement, velocity, and acceleration?

• A

• B

• C

• D

Two arrows are launched at the same time with the same speed. Arrow A at an angle greater than 45 degrees, and arrow B at an angle less than 45 degrees. Both land at the same spot on the ground. Which arrow arrives first?

• Arrow A arrives first.

• Arrow B arrives first.

• They both arrive together.

• It depends on the elevation where the arrows land.

An ideal elastic rubber ball is dropped from a height of about , hits the floor and rebounds to its original height. Which of the following graphs would best represent the distance above the floor versus time for the above bouncing ball?

• A

• B

• C

• D

A target (T) lies flat on the ground (3 m) from the side of a building that is (10 m) tall, as shown above. A student rolls a ball off the horizontal roof of the building in the direction of the target. Air resistance is negligible. The horizontal speed with which the ball must leave the roof if it is to strike the target is most nearly …  $g=10\ ms^{-2}$  

•  $\frac{3}{10}\ m/s$  

•  $\sqrt{2}\ m/s$  

•  $\frac{3}{\sqrt{2}}\ m/s$  

•  $3\ m/s$  

Starting from rest, (object 1) falls freely for (4.0 seconds), and (object 2) falls freely for (8.0 seconds). Compared to (object 1), (object 2) falls …

• half as far

• twice as far

• three times as far

• four times as far

A projectile is fired with initial velocity $(v_o)$  at an angle $(θ_o)$   with the horizontal and follows the trajectory shown . Which of the following pairs of graphs best represents the vertical components of the velocity and acceleration, (v) and (a), respectively, of the projectile as functions of time t?

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