A bullet is fired from a gun at 30\(^o\) to the horizontal. The bullet remains in flight for 25s before touching the ground. Calculating the velocity of pro...
Question 1 Report
A bullet is fired from a gun at 30\(^o\) to the horizontal. The bullet remains in flight for 25s before touching the ground. Calculating the velocity of projection. [g = 10ms\(^{-2}\)]
Answer Details
Projectile fired at an angle. For a projectile launched with speed u at angle \(\theta\) to the horizontal, the time of flight is
\[T=\dfrac{2u\sin\theta}{g}.\]
Given \(\theta=30^{\circ}\), \(T=25\,\text{s}\) and \(g=10\,\text{m s}^{-2}\):
\[25=\dfrac{2u\sin30^{\circ}}{10}=\dfrac{2u(0.5)}{10}=\dfrac{u}{10}.\]
Therefore \(u=25\times10=250\,\text{m s}^{-1}\).
The velocity of projection is \(250\,\text{m s}^{-1}\) at \(30^{\circ}\) to the horizontal.
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