Question

a body is projected at an angle 60° with the horizontal . it covers a horizontal distance of 100m. if the same body is projected at 60° with the vertical with the same velocity. the range is
1. 50m
2. 100m
3. 200m.
4. 150m​

Answer 1

Answer:

Therefore Range is 100m

Explanation:

Taking g = 10 m/s^2

CASE 1

Angle made with horizontal ($\theta$) = 60 degree

Range = 100 m

Initial velocity = u m/s

$R = \frac{u^2sin(2\theta)}{g}\\\\100 = \frac{u^2sin(120)}{10}\\\\1000 = u^2sin(60)\\1000 = u^2 \frac{\sqrt{3}}{2}\\u^2 = \frac{2000}{\sqrt{3}}\\u = \sqrt{\frac{2000}{\sqrt{3}}\\}$

CASE 2

Angle made with horizontal ($\theta$)= 90 - 60 = 30

Initial velocity = u

Range = >

Putting value of $u^2$ from the above

$R = \frac{u^2sin(2\theta)}{g}\\\\R = \frac{\frac{2000}{\sqrt{3}}sin(60)}{10}\\\\R = \frac{\frac{2000}{\sqrt{3}}\frac{\sqrt{3}}{2}}{10}\\\\R = \frac{1000}{10} = 100$