The range of the rifle bullet is 1000m, when theta is the angle of projection If the bullet is - Physics - Motion In A Plane

Question

The range of the rifle bullet is 1000m, when theta is the
angle of projection If the bullet is fired with same angle from a
car moving with 36km/hr towards the target, show that the range
will be increased by 1000/7(tanθ) 1/2

Jyoti Pant · Accepted Answer

Solution: Let the velocity of projection=u m/s $R = \frac{{2 u}^{2} \sin θ \cos θ}{g} = 1000 (g i v e n i n q u e s t i o n) o r R = \frac{2}{g} (u \cos θ) (u \sin θ) = \frac{2}{g} (H o r i z o n t a l v e l o c i t y) \times (I n i t i a l v e r t i c a l v e l o c i t y) N o w n e w h o r i z o n t a l v e l o c i t y w i l l b e (u \cos θ) + 10 (\sin c e 36 k m / h = 10 m / s) V e r t i c a l v e l o c i t y = (u \sin θ) T h e r e f o r e R' = \frac{2}{g} (u \cos θ + 10) (u \sin θ) N o w R' - R = \frac{2}{g} (u \cos θ + 10) (u \sin θ) - \frac{2}{g} (u \cos θ) (u \sin θ)$ $= \frac{20 u \sin θ}{g} = \frac{20 \sin θ}{g} \sqrt{\frac{500 \times 9 8}{\sin θ \cos θ}} (P u t t i n g t h e v a l u e o f u a n d g) = \frac{1000 \sqrt{\tan θ}}{7} m$ Hence the range is increased by the above given factor

The range of the rifle bullet is 1000m, when theta is the angle of projection. If the bullet is fired with same angle from a car moving with 36km/hr towards the target, show that the range will be increased by 1000/7(tanθ) 1/2.

The range of the rifle bullet is 1000m, when theta is the angle of projection. If the bullet is fired with same angle from a car moving with 36km/hr towards the target, show that the range will be increased by 1000/7(tanθ) ^1/2.