Chapter #4 :Motion in Two Dimensions : Short Q/A / C.R.Q's

Q.  Prove that 2αθ=ω_f² - ω_i²

Ans. As we know that a/c to third equation of motion

                        2as=V_f² –V_i²

But a=rα  , V=rω and S=rθ     so putting in third equation of motion

                        2(rα)(rθ)=( rω_f) ²–( rω_i) ²

                        r² (2αθ)= r² (ω_f² - ω_i²)

then                       2αθ=ω_f² - ω_i²

Q. At what point in the path of projectile the velocity of projectile is (1) Maximum (2) Minimum

Ans. When a projectile is fired the x component of its velocity remains constant and when the projectile is moving upward the y component of velocity decreases and during fall it increases. But over all the projectile has the minimum velocity at the maximum height and maximum velocity when it is fired and when it is about to hit the ground.

Q. When mud flies off the tyre of a moving bicycle, in what direction does it fly?

Ans. During circular motion the body is to go out of the circular path. so when the force applied on it, is removed the tangential component of velocity work out and therefore the mud flies of the tyre making a tangent with the tyre at a point.

Q. Write two angles for which the range will be same? How we can determine these angles?

Ans. The two angles for which the range is same if both has the same velocity are 40 and 50 degrees.

The method to determine is that” Every two angles have the same range is the difference of two angles with 45 is same. for example (30 and 60 ,70 and 20 ,80 and 10)