Question

2. Find the minimum velocity with which a Stone in to be projected in order to hit a Target at 20m away?​

Answer 1

Answer:

7$\sqrt{2}$ i + 7$\sqrt{2}$ j m/s is the minimum velocity with which the stone should be profected

Explanation:

The formla for horizontal range is: R = $\frac{u^{2}sin(2\theta)}{g}$

where u is the speed of projection and θ is the angle of projection

Thus more maximum value of sin2θ we get the minimum value of u for a constant range.

in our case the range is 20m and the maximum value of sin2θ is 1 for θ= pi/4

so

$\frac{u^{2} }{g} = 20$

u= $\sqrt{20g}$

u= $\sqrt{196}$

u= 14m/s (minimum speed)

u= 7$\sqrt{2}$ i + 7$\sqrt{2}$ j (minimum velocity)

Thus we obtain the minimum speed and velocity.

Hope this helps!!!