Solve the following :

Question:

One man is sitting on the shores of a river. He is in the line of $1.0 \mathrm{~m}$ long boat and is $5.5 \mathrm{~m}$ away from the center of the boat. If he can throw the apply only with a speed of $10 \mathrm{~m} / \mathrm{s}$. find the minimum and maximum angles of projection for successful shot. Assume that the point of projection and the edge pf the boat are in the same horizontal level.

Solution:

For near point of boat

$R=5 m=\frac{u^{2} \sin 2 \theta}{g} g$

$5=\frac{(10)^{2} \sin 2 \theta}{\text { g }}$

$\theta=15^{\circ}$ or $75^{\circ}$

For for point of boat

$=\frac{\mathrm{u}^{2} \sin 2 \theta}{\mathrm{g}}$

$6=\frac{(10)^{2} \sin 2 \theta}{\mathrm{g}}$

$\theta=18^{\circ}$ or $71^{\circ}$

For a successful shot angle may vary from $15^{\circ}$ to $18^{\circ}$ or $71^{\circ}$ to $75^{\circ}$

Minimum angle $=15^{\circ}$

Maximum angle $=75^{\circ}$

 

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